<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="12" minor="2"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false"><Zoom percentage="150"/></View-Properties>
<MapleNet-Properties warnlevel="3" longdelim="true" plotoptions="" echo="1" errorcursor="false" elisiontermsthreshold="10000" elisiontermsbefore="100" errorbreak="1" prettyprint="3" prompt="> " latexwidth="6.0" useclientjvm="true" ansi="false" screenheight="25" labelwidth="20" plotdevice="inline" typesetting="standard" displayprecision="-1" indentamount="4" elisiondigitsthreshold="10000" quiet="false" plotoutput="terminal" rtablesize="10" preplot="" showassumed="1" plotdriver="openviz" elisiontermsafter="100" labelling="true" postplot="" screenwidth="79" elisiondigitsbefore="100" elisiondigitsafter="100" verboseproc="1" imaginaryunit="I" ShowLabels="true"/>
<Styles><Font name="Heading 4" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[40,120,40]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="16" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Code" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Header and Footer" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="newline" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.3" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
</Styles>
<Task-table>
<Task-category name="<default>">
</Task-category>
</Task-table>
<Task>
</Task>
<Group labelreference="L376" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">restart; Digits:=14: with(LinearAlgebra):</Text-field>
</Input>
</Group>
<Group labelreference="L324" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">with(orthopoly):</Text-field>
</Input>
</Group>
<Group labelreference="L384" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Laguerre basis set for central potentials.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L383" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">L(2,1,x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgiIiQiIiJJInhHNiIhIiQqJEYlIiIjI0YkRik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L317" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Radial orbitals (multiplied by r, leaving out Y_Lm): look almost like hydrogenic orbitals, but form an enumerably infinite set.</Text-field>
</Input>
</Group>
<Group labelreference="L347" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">uL:=(n,l,beta)->r^(l+1)*exp(-beta*r/2)*L(n-1,2*l+2,beta*r);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2JUkibkc2IkkibEdGJUklYmV0YUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKigpSSJyR0YlLCY5JSIiIkYwRjBGMC1JJGV4cEdGJTYjLCQqJjkmRjBGLUYwIyEiIiIiI0YwLUkiTEdGJTYlLCY5JEYwRjhGMCwmRi9GOUY5RjBGNUYwRiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L356" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">plot([seq(uL(n,0,1.5),n=1..4)],r=0..20,color=[red,blue,green,black]);</Text-field>
<Text-field style="Maple Plot" layout="Maple Plot"></Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="384" type="two-dimensional" width="716" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">6)-%'CURVESG6$7eo7$$""!!""$""!!""7$$"2KLL3FWYs#!#=$"2b`@#\;`pE!#=7$$"2kmm;a)G\a!#=$"29'pXJw1J_!#=7$$",D"G$R<)!#7$"1X-3jY)yo(!#<7$$"2LLL$3x&)*3"!#<$"2txh(3rJ/5!#<7$$",Dc'yM;!#6$"2&f]x(pZhW"!#<7$$"2mmmmT:(z@!#<$"2kySc"3)4&=!#<7$$"1LL$3FWYs#!#;$"2dw-))4r5A#!#<7$$"+DJdpK!#5$"1US"z$>beD!#;7$$"1nm;z>]9Q!#;$"1r)>HdTa'G!#;7$$"1LLLL3VfV!#;$"12OT%*)[O9$!#;7$$"1mm"z>5xI&!#;$"2x'=^"R3Zc$!#<7$$",Dc*)fD'!#6$"2Y!)Qy)*RJ"R!#<7$$"1LL3F*oU?(!#;$"1brE#=Jp>%!#;7$$"1nmm"H[D:)!#;$"0d&*y1:LU%!#:7$$"-v$pU&G5!#6$"2ES9B;"fbZ!#<7$$"2LLL$e0$=C"!#;$"10Tx&GmH*[!#;7$$"2LL$3xf]&H"!#;$"0(eHsu/.\!#:7$$"2MLLeR"=\8!#;$"2YHf-Y:Z!\!#<7$$"2OL$e9o&GS"!#;$"1QYSu%=')*[!#;7$$"2NLLLBKlX"!#;$"1MHd$om`)[!#;7$$"2OLL32$)Qc"!#;$"1<lX[4mR[!#;7$$"2OLL$3RBr;!#;$"1/J9U=zrZ!#;7$$"2-+]P9:\)=!#;$"22ur%>2'\e%!#<7$$"2mmm"zjf)4#!#;$"1BL?w'G)[V!#;7$$",vB1nH#!#5$"2a9?F#HB-T!#<7$$"2MLLe4;[\#!#;$"28B#\p#G3%Q!#<7$$"1nm;zt%**p#!#:$"29Ss(e\!Rc$!#<7$$",Dmy]!H!#5$"2w'3m0*eyG$!#<7$$"1nm;HdA<J!#:$"2Nu>)eU+4I!#<7$$"2PLLezs$HL!#;$"1C*HLaX5u#!#;7$$"2nmmT]R3a$!#;$"2)Re(GH-w[#!#<7$$",D@1Bv$!#5$"2)e7=G2a\A!#<7$$"1MLe9d#)pR!#:$"1,7+,&)p@?!#;7$$"1nmm;_M(=%!#:$"1%)e9\!y9"=!#;7$$"1MLL3y_qX!#:$"2V%G$43sL["!#<7$$"20+++l+>+&!#;$"2Ef<wieY<"!#<7$$"*vW]V&!")$"08_%z")\B#*!#;7$$"*NfC&e!")$"1:*==6NAE(!#<7$$"1ML$ez6:B'!#:$"1\#[1Uc">e!#<7$$"1nmm;=C#o'!#:$"1P!4'f-<]W!#<7$$"1nmmm#pS1(!#:$"2:-$>=A(H`$!#=7$$",DOD#3v!#5$"28mGiFN7p#!#=7$$"1mmmm(y8!z!#:$"1RG]ZX"*3@!#<7$$"1,+]i.tK$)!#:$"215?g*HK4;!#=7$$",v3zMu)!#5$"2;6<?')R4C"!#=7$$"1omm"H_?<*!#:$"1PYD]cDR%*!#=7$$"1nm;zihl&*!#:$"11[;#R8"Gt!#=7$$"1LLL3#G,***!#:$"1nI`iYWmb!#=7$$"2ML$ezw5V5!#:$"1[:JPG^vT!#=7$$"-v$Q#\"3"!#5$"1&3-q29iC$!#=7$$"2NLLe"*[H7"!#:$"1G#>7%*4*pC!#=7$$"*dxd;"!"($"2jnrJ+m'f=!#>7$$",D0xw?"!"*$"2i_qC+-qS"!#>7$$"2,+]i&p@[7!#:$"2)*R5eqoH2"!#>7$$",vgHKH"!"*$"1Vc%3"4`Jz!#>7$$"2lmmmZvOL"!#:$"00h_%*f$Rg!#=7$$"2,++]2goP"!#:$"1%p&y)*[#*4X!#>7$$"2KL$eR<*fT"!#:$"2b8.&f)R%eM!#?7$$"2-++])Hxe9!#:$"2j6AiU&*\e#!#?7$$"2mm;H!o-*\"!#:$"2()RiXg7T'>!#?7$$"2,+]7k.6a"!#:$"28P&>AHxs9!#?7$$"2mmm;WTAe"!#:$"2ZCuJ*Hm56!#?7$$"-D1*3`i"!#5$"10vT")zsf#)!#?7$$"2NLLL*zym;!#:$"1Qu%=9"*e?'!#?7$$"2OLL3N1#4<!#:$"1>%G9)**pHY!#?7$$"1nm"HYt7v"!#9$"1()QU!Q=,Y$!#?7$$"2-+++xG**y"!#:$"2yB3=%RXYE!#@7$$"1nm;9@BM=!#9$"1nA&3(*f_%>!#?7$$"2OLLLbdQ(=!#:$"2&e4'GvdjZ"!#@7$$"-DOl5;>!#5$"2-2X@Nm'*4"!#@7$$"2-+]P?Wl&>!#:$"111f%4$>"H)!#@7$$"$+#!""$"1;l.5k/=h!#@-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'CURVESG6$7jo7$$""!!""$""!!""7$$"2KLL3FWYs#!#=$"16n&f3#\**y!#<7$$"2kmm;a)G\a!#=$"2e"*zS*=cE:!#<7$$",D"G$R<)!#7$"1tY')>]57A!#;7$$"2LLL$3x&)*3"!#<$"2:2'*["pw[G!#<7$$",Dc'yM;!#6$"2;Bo(p;#Q)R!#<7$$"2mmmmT:(z@!#<$"0R^Rt]x%\!#:7$$"1LL$3FWYs#!#;$"1H$Q(***oav&!#;7$$"+DJdpK!#5$"1jSZ:*\3U'!#;7$$"1nm;z>]9Q!#;$"0A'4O)*ycp!#:7$$"1LLLL3VfV!#;$"1$o=`po_P(!#;7$$"1mm"z>5xI&!#;$"1/;?7$fg&y!#;7$$",Dc*)fD'!#6$"1u#Qa_Nt1)!#;7$$"1m;zW#H,t'!#;$"1w4hn%>m3)!#;7$$"1LL3F*oU?(!#;$"13V(4T?a0)!#;7$$".v$4'3%yw!#8$"1xsdJZhyz!#;7$$"1nmm"H[D:)!#;$"1$RX'[<vgy!#;7$$"-v$pU&G5!#6$"1&Q_-n!yHp!#;7$$"2LLL$e0$=C"!#;$"1m(oaFYXc&!#;7$$"2MLLeR"=\8!#;$"1P4_/,7)y%!#;7$$"2NLLLBKlX"!#;$"1#o.8)*eD)R!#;7$$"2OLL32$)Qc"!#;$"1RId1r)f;$!#;7$$"2OLL$3RBr;!#;$"2jS#GJ]?`B!#<7$$"2omTg_u!y<!#;$"1D_OyV))f:!#;7$$"2-+]P9:\)=!#;$"1,XozJ*["z!#<7$$"2MLe9wb<*>!#;$"1V&)=5O&*Hb!#=7$$"2mmm"zjf)4#!#;$!1OsM;9oJk!#<7$$",vB1nH#!#5$!2LQtP9Pd#=!#<7$$"2MLLe4;[\#!#;$!1mYhtav]G!#;7$$"1nm;zt%**p#!#:$!1ZxB.*==u$!#;7$$",Dmy]!H!#5$!2vPO7TcOY%!#<7$$"1nm;HdA<J!#:$!1U#)olagU]!#;7$$"2PLLezs$HL!#;$!1-X;mq!eY&!#;7$$"2nmmT]R3a$!#;$!14!y_#Q\\d!#;7$$",D@1Bv$!#5$!1"p&*)*GEG"f!#;7$$"1n;ajf1hQ!#:$!1M?&Q[oc&f!#;7$$"1MLe9d#)pR!#:$!075;a!ftf!#:7$$".DcY&eyS!#7$!1Cxii!=)of!#;7$$"1nmm;_M(=%!#:$!1uQ%)o<\Vf!#;7$$"1,+]7l$*yV!#:$!1Jw!**)e1be!#;7$$"1MLL3y_qX!#:$!1TZ@wPd>d!#;7$$"20+++l+>+&!#;$!0/gmu7$*G&!#:7$$"*vW]V&!")$!20C%p\$pCv%!#<7$$"*NfC&e!")$!2<wjP$)>m>%!#<7$$"1ML$ez6:B'!#:$!1_eObVd$p$!#;7$$"1nmm;=C#o'!#:$!1oT7#*f^DJ!#;7$$"1nmmm#pS1(!#:$!2jw?XS#o$o#!#<7$$",DOD#3v!#5$!16mug&*eBA!#;7$$"1mmmm(y8!z!#:$!1a@qHb#o'=!#;7$$"1,+]i.tK$)!#:$!1%*[***G6(G:!#;7$$",v3zMu)!#5$!2%HOD,yBb7!#<7$$"1omm"H_?<*!#:$!2\aqn_#[:5!#<7$$"1nm;zihl&*!#:$!1(>,j4aiJ)!#<7$$"1LLL3#G,***!#:$!1(zMx(4\rm!#<7$$"2ML$ezw5V5!#:$!2/C/!4/h!G&!#=7$$"-v$Q#\"3"!#5$!1h!\tZpAH%!#<7$$"2NLLe"*[H7"!#:$!1)Q"o`5S>M!#<7$$"*dxd;"!"($!228K.dNSp#!#=7$$",D0xw?"!"*$!2kkmgW0n7#!#=7$$"2,+]i&p@[7!#:$!2'=TV')f0(o"!#=7$$",vgHKH"!"*$!1&o!ojwk+8!#<7$$"2lmmmZvOL"!#:$!2#4eqR6+F5!#=7$$"2,++]2goP"!#:$!0&R%>$eKhz!#<7$$"2KL$eR<*fT"!#:$!1MB]^9:3j!#=7$$"2-++])Hxe9!#:$!1UaJ8O)3)[!#=7$$"2mm;H!o-*\"!#:$!0`4fP_r#Q!#<7$$"2,+]7k.6a"!#:$!1Bf.$p6F'H!#=7$$"2mmm;WTAe"!#:$!2YZO`i1GI#!#>7$$"-D1*3`i"!#5$!2d]n#y&**ew"!#>7$$"2NLLL*zym;!#:$!1F$>A**3aO"!#=7$$"2OLL3N1#4<!#:$!2/rj@*e2[5!#>7$$"1nm"HYt7v"!#9$!1dE:LZQ^!)!#>7$$"2-+++xG**y"!#:$!1O7%3*)4:J'!#>7$$"1nm;9@BM=!#9$!2L`a@Z4&oZ!#?7$$"2OLLLbdQ(=!#:$!19G2k)=oq$!#>7$$"-DOl5;>!#5$!1Cb">#prIG!#>7$$"2-+]P?Wl&>!#:$!2KFre2xX=#!#?7$$"$+#!""$!2#f)42`s=l"!#?-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%'CURVESG6$7ep7$$""!!""$""!!""7$$"2KLL3FWYs#!#=$"2i2:Zz+$e:!#<7$$"2kmm;a)G\a!#=$"1&e*p=XNpH!#;7$$",D"G$R<)!#7$"1(Q]m'yYTU!#;7$$"2LLL$3x&)*3"!#<$"0=*[I`e#Q&!#:7$$"2lm;a8ABO"!#<$"1P0mEFI+k!#;7$$",Dc'yM;!#6$"1%)Hxn-)=I(!#;7$$"2ML$e*)4D2>!#<$"18>%G>bU4)!#;7$$"2mmmmT:(z@!#<$"0(4(*pR0%y)!#:7$$"+DJdpK!#5$"2brc2!*yR1"!#;7$$"1LLLL3VfV!#;$"2=&*3l.I68"!#;7$$"2k;zWn+lf%!#<$"1tOXv[3L6!#:7$$".Dc^qN$[!#8$"2#)=PKbR68"!#;7$$"1K3xc.kq]!#;$"2)Q)Q;u`b7"!#;7$$"1mm"z>5xI&!#;$"1TDPBfd;6!#:7$$"1L$3-))\=y&!#;$"2Ggi2e%Q*3"!#;7$$",Dc*)fD'!#6$"2GH^=8W80"!#;7$$"1LL3F*oU?(!#;$"14>$>8[1\*!#;7$$"1nmm"H[D:)!#;$"1=vz,*>0@)!#;7$$"1MLe9w)*=#*!#;$"1<+Js]myl!#;7$$"-v$pU&G5!#6$"113!RZ$QX[!#;7$$"2lmTgi'=N6!#;$"2;BoB`/U4$!#<7$$"2LLL$e0$=C"!#;$"1tz!Rb[#*Q"!#;7$$"2MLLeR"=\8!#;$!2t**Hh`[!=B!#=7$$"2NLLLBKlX"!#;$!2:=lwr'>A<!#<7$$"2OLL32$)Qc"!#;$!2`"o3&))[z0$!#<7$$"2OLL$3RBr;!#;$!2&eM;;ACCU!#<7$$"2-+]P9:\)=!#;$!13GXNaj<g!#;7$$"2mmm"zjf)4#!#;$!1.$p%=1&)=r!#;7$$"2OLL$38l(>#!#;$!10K!3(pt4u!#;7$$",vB1nH#!#5$!1^)3*Ge!Gd(!#;7$$"2NL$3-PBYB!#;$!1)[ga5Z$4w!#;7$$"2lmmm;hdR#!#;$!1xrrdla<w!#;7$$"-DJ')GXC!#6$!1=<Lz8o)f(!#;7$$"2MLLe4;[\#!#;$!1w3j2"[Sb(!#;7$$"1nm;zt%**p#!#:$!1">=/4pL7(!#;7$$",Dmy]!H!#5$!1`;#)QYZlj!#;7$$"1nm;HdA<J!#:$!1R.pFa"3L&!#;7$$"2PLLezs$HL!#;$!0([QlR!y7%!#:7$$"2nmmT]R3a$!#;$!2EwyL&=hOG!#<7$$",D@1Bv$!#5$!2oTa7qDj^"!#<7$$"1MLe9d#)pR!#:$!1fPq,5R4=!#<7$$"1nmm;_M(=%!#:$"2;1'fvBk*3"!#<7$$"1,+]7l$*yV!#:$"0=in8X.8#!#:7$$"1MLL3y_qX!#:$"1il1&o5@3$!#;7$$"1nm;HU@'y%!#:$"0lmi")*\NS!#:7$$"20+++l+>+&!#;$"2mh-6%G>d[!#<7$$"*vW]V&!")$"1v-H!f9x5'!#;7$$"*0_Pk&!")$"1&*fZ5Y7Gl!#;7$$"*NfC&e!")$"1(Q(>(QD&Ro!#;7$$"1nm"Hd&)>/'!#:$"1C#=>jp_.(!#;7$$"1ML$ez6:B'!#:$"1#\v;x/c:(!#;7$$"1n;/,V>Wj!#:$"0W$oD`Y%>(!#:7$$"-D1o(oX'!#6$"0D'[:!)*3@(!#:7$$"1M$e9Jf&pl!#:$"1:0=(R"[1s!#;7$$"1nmm;=C#o'!#:$"1<EnEZx#=(!#;7$$"1ommTb:to!#:$"1:'*QnU'G5(!#;7$$"1nmmm#pS1(!#:$"1o5U_p8zp!#;7$$",DOD#3v!#5$"1F,ae%\(el!#;7$$"1mmmm(y8!z!#:$"1ySr%pq%zg!#;7$$"1,+]i.tK$)!#:$"1*\P=cx0\&!#;7$$",v3zMu)!#5$"1.))Q;O72\!#;7$$"1omm"H_?<*!#:$"2NuHf(*[_I%!#<7$$"1nm;zihl&*!#:$"2$>rVU>FxP!#<7$$"1LLL3#G,***!#:$"1M:D^$4tC$!#;7$$"2ML$ezw5V5!#:$"2YFz!e')R[F!#<7$$"-v$Q#\"3"!#5$"11W2")>yfB!#;7$$"2NLLe"*[H7"!#:$"0_%)phgz)>!#:7$$"*dxd;"!"($"2#4f(yz!3a;!#<7$$",D0xw?"!"*$"2)zt#>j)\t8!#<7$$"2,+]i&p@[7!#:$"2r">6*Q+:9"!#<7$$",vgHKH"!"*$"1Mt6%QyYC*!#<7$$"2lmmmZvOL"!#:$"1BUc5Nb9w!#<7$$"2,++]2goP"!#:$"2ac%3IMCjh!#=7$$"2KL$eR<*fT"!#:$"2&3yv*H..2&!#=7$$"2-++])Hxe9!#:$"2O7.Q.!3"3%!#=7$$"2mm;H!o-*\"!#:$"1A^q4K];L!#<7$$"2,+]7k.6a"!#:$"2&*z"\;[hhE!#=7$$"2mmm;WTAe"!#:$"2$>A$[XN.9#!#=7$$"-D1*3`i"!#5$"1pp`ZZt)p"!#<7$$"2NLLL*zym;!#:$"2J!y*3SCiN"!#=7$$"2OLL3N1#4<!#:$"2U2o_&*pX2"!#=7$$"1nm"HYt7v"!#9$"1bC=eVQ5&)!#=7$$"2-+++xG**y"!#:$"1$yz*p0Hbo!#=7$$"1nm;9@BM=!#9$"1C*)HS'3'Q`!#=7$$"2OLLLbdQ(=!#:$"1y)\J"yogU!#=7$$"-DOl5;>!#5$"2Z!e]r@zVL!#>7$$"2-+]P?Wl&>!#:$"1%4rH:&3ZE!#=7$$"$+#!""$"2$pAx$fjc0#!#>-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%'CURVESG6$7^r7$$""!!""$""!!""7$$"2mm;a8ABO"!#=$"2x%ohV$e5K"!#<7$$"2KLL3FWYs#!#=$"1R[a*\S:c#!#;7$$"-D1k'p3%!#8$"1<B9(*\JCP!#;7$$"2kmm;a)G\a!#=$"1**zTqO<7[!#;7$$",D"G$R<)!#7$"1;h&)Gw$Rx'!#;7$$"2LLL$3x&)*3"!#<$"1WN&*yspn%)!#;7$$"2lm;a8ABO"!#<$"1(*)HgQ'>8**!#;7$$",Dc'yM;!#6$"2G!48h2"H6"!#;7$$"2ML$e*)4D2>!#<$"2-5u!e!3L@"!#;7$$"2mmmmT:(z@!#<$"2A:Pe!)yTH"!#;7$$"1LL$3FWYs#!#;$"1)f4*fxa.9!#:7$$"+DJdpK!#5$"2Zth?FmDX"!#;7$$"2OL$3_v.UN!#<$"2d()ej8&pd9!#;7$$"1nm;z>]9Q!#;$"2$pO4cg[^9!#;7$$"-D1k'p3%!#7$"2k&zBTs.N9!#;7$$"1LLLL3VfV!#;$"1M<E,,Q49!#:7$$"1mm"z>5xI&!#;$"2$\2[vhah7!#;7$$",Dc*)fD'!#6$"2#[]:v;j[5!#;7$$"1m;zW#H,t'!#;$"1`wAx"QvE*!#;7$$"1LL3F*oU?(!#;$"1&yq9-Ec)z!#;7$$".v$4'3%yw!#8$"1ENAh6!em'!#;7$$"1nmm"H[D:)!#;$"1j*y$RW/I`!#;7$$"1,]7`zw&o)!#;$"1/;"y)=RKQ!#;7$$"1MLe9w)*=#*!#;$"2-MUP>W;O#!#<7$$"1n;/ws?_(*!#;$"1R-'p2m-P*!#<7$$"-v$pU&G5!#6$!2NM,:tYlD%!#=7$$"2K$e*)fY'=3"!#;$!1r3^0oj8<!#;7$$"2lmTgi'=N6!#;$!1XI#*eu&o"H!#;7$$"/v=#f3&)="!#8$!2O$e"fLUw-%!#<7$$"2LLL$e0$=C"!#;$!169_G2US]!#;7$$"2MLLeR"=\8!#;$!1dc9LZmon!#;7$$"2NLLLBKlX"!#;$!1iN"R8?V2)!#;7$$"2OLL32$)Qc"!#;$!1x%p3'HRl*)!#;7$$"2OLL$3RBr;!#;$!0&=4lMKk%*!#:7$$"1</wiS%zp"!#:$!1F5EwN:J&*!#;7$$"2,](=<UlC<!#;$!1M#y"[!eid*!#;7$$"2Ne9;Pk8v"!#;$!0*p>@8B+'*!#:7$$"2omTg_u!y<!#;$!1AkL6lo.'*!#;7$$"2-vo/o%y/=!#;$!0$e>MGD(e*!#:7$$"2N$e*[$[\J=!#;$!1&f&4"=t:b*!#;7$$"1<HK*)\?e=!#:$!1f5jS=I(\*!#;7$$"2-+]P9:\)=!#;$!1t')3fB5D%*!#;7$$"2MLe9wb<*>!#;$!1$Q8)p!40(*)!#;7$$"2mmm"zjf)4#!#;$!1&QT]&oH$G)!#;7$$",vB1nH#!#5$!1$\SW))3$Rl!#;7$$"2MLLe4;[\#!#;$!2')Rx"\X7-W!#<7$$",vt"Q(f#!#5$!1NO#\zqt@$!#;7$$"1nm;zt%**p#!#:$!2'=(p+#=u:?!#<7$$"2NLL3-8D!G!#;$!1"fkU;,L@)!#<7$$",Dmy]!H!#5$"1N#3O***p[M!#<7$$"1nm;HdA<J!#:$"1,5HF@e$f#!#;7$$"2PLLezs$HL!#;$"2ckIMG*pFX!#<7$$"2nmmT]R3a$!#;$"1Ad.IWApg!#;7$$",D@1Bv$!#5$"1De4eU`!>(!#;7$$"1n;ajf1hQ!#:$"1=RI%yv8g(!#;7$$"1MLe9d#)pR!#:$"0d(R,Xu,z!#:7$$"1nT5!f0U-%!#:$"17K+N'=:,)!#;7$$".DcY&eyS!#7$"14t'R$Q/&4)!#;7$$"1Me9T`'H8%!#:$"1/i6a">H:)!#;7$$"1nmm;_M(=%!#:$"0"z^t,!e=)!#:7$$"1,]iSICNU!#:$"1(4Gu=>Y>)!#;7$$"1MLek39$G%!#:$"1cFY3_5&=)!#;7$$"1o;a)oQ5L%!#:$"1Z]M,Fzd")!#;7$$"1,+]7l$*yV!#:$"1d7>(yOK6)!#;7$$"1omTg@tuW!#:$"1Y1$o2-Z(z!#;7$$"1MLL3y_qX!#:$"0'fapODux!#:7$$"1nm;HU@'y%!#:$"1"=-`e')>7(!#;7$$"20+++l+>+&!#;$"1TidV*o#Qi!#;7$$")FZ=_!"($"1yJ_CN9v^!#;7$$"*vW]V&!")$"1p^P%y3,*R!#;7$$"*0_Pk&!")$"2W0JVnY"zF!#<7$$"*NfC&e!")$"2`Qz3`j.a"!#<7$$"1nm"Hd&)>/'!#:$"1W\=`'e#*>%!#<7$$"1ML$ez6:B'!#:$!1UgW%H3%Rn!#<7$$"-D1o(oX'!#6$!2#*>?]:%o:>!#<7$$"1nmm;=C#o'!#:$!2M7*RnkNrI!#<7$$"1ommTb:to!#:$!1jh'))*e:qR!#;7$$"1nmmm#pS1(!#:$!0[<<Ldwy%!#:7$$",DOD#3v!#5$!1Vz&yp\PN'!#;7$$"1mmmm(y8!z!#:$!1&)Ri-!oNM(!#;7$$"1MLekX0<")!#:$!1'HxD'[*\t(!#;7$$"1,+]i.tK$)!#:$!0f6V"=7E!)!#:7$$"+DZ5Q&)!"*$!1(4&*=DFl@)!#;7$$",v3zMu)!#5$!1DxD`31H$)!#;7$$"1NLe*olx&*)!#:$!11ln^59r$)!#;7$$"1omm"H_?<*!#:$!1)>R<sEWM)!#;7$$"1omT&GM)o$*!#:$!1@k`.jOm#)!#;7$$"1nm;zihl&*!#:$!1-z%)z&)\V")!#;7$$"1LLL3#G,***!#:$!1(RwA4JRv(!#;7$$"2ML$ezw5V5!#:$!1*)G%R9nt@(!#;7$$"-v$Q#\"3"!#5$!1H@RY1(>o'!#;7$$"2NLLe"*[H7"!#:$!1BfN%='Rng!#;7$$"*dxd;"!"($!1'yN7'[sAa!#;7$$",D0xw?"!"*$!2c4)yHIK0[!#<7$$"2,+]i&p@[7!#:$!2%=$e,+fdB%!#<7$$",vgHKH"!"*$!1Gki(eMsk$!#;7$$"2lmmmZvOL"!#:$!1&pVO+4S;$!#;7$$"2,++]2goP"!#:$!1jd"4w?()p#!#;7$$"2KL$eR<*fT"!#:$!1og&)QVdAB!#;7$$"2-++])Hxe9!#:$!2w]-a>a$f>!#<7$$"2mm;H!o-*\"!#:$!2/"pPaT)3m"!#<7$$"2,+]7k.6a"!#:$!2*)*\*G'eO!R"!#<7$$"2mmm;WTAe"!#:$!2xm'QL![J;"!#<7$$"-D1*3`i"!#5$!1v*=Y)en0'*!#<7$$"2NLLL*zym;!#:$!1v*>Sg9h&z!#<7$$"2OLL3N1#4<!#:$!1</)=hNi`'!#<7$$"1nm"HYt7v"!#9$!1/%oh*p*)e`!#<7$$"2-+++xG**y"!#:$!1"4&3W'>:X%!#<7$$"1nm;9@BM=!#9$!1*[.3Booe$!#<7$$"2OLLLbdQ(=!#:$!2%\rFziP[H!#=7$$"-DOl5;>!#5$!2mO)>_*pbQ#!#=7$$"2-+]P?Wl&>!#:$!2cEM(f')yU>!#=7$$"$+#!""$!1v#\")y$)Rb"!#<-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%%VIEWG6$;$""!!""$"$+#!""%(DEFAULTG-%+AXESLABELSG6'-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"r6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%%FONTG6%%(DEFAULTG%(DEFAULTG"#5%+HORIZONTALG%+HORIZONTALG-%%ROOTG6'-%)BOUNDS_XG6#$"$q&!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%qk!""-%.BOUNDS_HEIGHTG6#$"%?P!""-%)CHILDRENG6"</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L377" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">int(uL(1,0,1.5)^2,r=0..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIvZiNmI2YjZiNmISM5</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L330" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">This basis is orthogonal, but not yet normalized. Orthogonality is demonstrated below.</Text-field>
</Input>
</Group>
<Group labelreference="L326" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">int(uL(1,0,1.5)*uL(2,0,1.5),r=0..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIiIUYj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L341" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Define a basis with fixed parameter beta:</Text-field>
</Input>
</Group>
<Group labelreference="L358" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">phi:=n->uL(n,0,3/2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkjdUxHRiU2JTkkIiIhIyIiJCIiI0YlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L337" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">OL:=(m,n)->int(phi(n)*phi(m),r=0..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2JEkibUc2IkkibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJi1JJHBoaUdGJTYjOSUiIiItRjI2IzkkRjUvSSJyR0YlOyIiIUkpaW5maW5pdHlHRi1GJUYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L351" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">OL(2,2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IyIjOyIiKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L423" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># a few orthogonality checks:</Text-field>
</Input>
</Group>
<Group labelreference="L349" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">OL(1,2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L344" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">OL(2,4);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L370" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Now define the exponential potential and its matrix elements:</Text-field>
</Input>
</Group>
<Group labelreference="L375" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">V0:=-2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">ISIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L388" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r0:=4.0; # to be consistent with the potential used in PH5000L5.mw where phase shifts are calculated.</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjcjBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEkNC4wRidGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5">JCIjUyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L348" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">V:=V0*exp(-r/r0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJyR0YoJCEvKysrKysrRCEjOSEiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L352" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VME:=(m,n)->int(phi(n)*V*phi(m),r=0..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkVk1FRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYoLUkobWZlbmNlZEdGJDYkLUYjNigtRiw2JVEibUYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRIm5GJ0YvRjIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRj1GOUY5LUY2Ni1RKCYjODU5NDtGJ0Y5RjtGPkZARkJGREZGRkhGZ24vRk5GaG4tRiM2Ki1JKG1zdWJzdXBHRiQ2Jy1GNjYtUSgmIzg3NDc7RidGOUY7Rj5GQEZCRkRGRkZIRmduRmZvLUkjbW5HRiQ2JFEiMEYnRjktRiw2JVEoJiM4NzM0O0YnRi9GMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIyRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GIzYoLUYjNigtRiw2JVEnJiM5NjY7RicvRjBGPUY5LUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZnbkZmby1GUjYkLUYjNiZGW29GXm9GYW9GOUY5Rl5vRmFvRjktRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSEZnbkZmby1GLDYlUSJWRidGL0YyRltyLUYjNihGYHFGZHEtRlI2JC1GIzYmRlZGXm9GYW9GOUY5Rl5vRmFvRjlGOS1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4zZW1GJy8lJmRlcHRoR0Zccy8lKmxpbmVicmVha0dRJWF1dG9GJy1GNjYtUTAmRGlmZmVyZW50aWFsRDtGJ0Y5RjtGPkZARkJGREZGRkhGZ25GZm8tRiw2JVEickYnRi9GMkZeb0Zhb0Y5Rl5vRmFvRjlGXm9GYW9GOQ==">Zio2JEkibUc2IkkibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqKC1JJHBoaUdGJTYjOSUiIiJJIlZHRiVGNS1GMjYjOSRGNS9JInJHRiU7IiIhSSlpbmZpbml0eUdGLUYlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L345" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VME(1,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEvP0peb2JqdSEjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L366" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Had we defined the basis with a non-float (using 15/10 instead of 1.5) the numbers would be computed symbolically exactly.</Text-field>
</Input>
</Group>
<Group labelreference="L329" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VME(2,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEvMyo+QW4nKT4kISM5</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L333" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VME(3,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEvIilvMCNcIVIiKiEjOg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L355" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VME(1,6);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEvdidSVGdiSyohIzw=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L381" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TME:=(m,n)->-1/2*int(phi(n)*diff(phi(m),r$2),r=0..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2JEkibUc2IkkibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQtSSRpbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JComLUkkcGhpR0YlNiM5JSIiIi1JJWRpZmZHRi42JC1GMzYjOSQtSSIkR0YuNiRJInJHRiUiIiNGNi9GQDsiIiFJKWluZmluaXR5R0YuIyEiIkZBRiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L332" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TME(1,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IyIiIiIiJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L342" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TME(1,3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IyIiIiIiJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L321" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TME(1,2),TME(2,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQjIiIiIiIkRiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L364" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TME(10,10);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IyIkOigiIic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L338" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TME(10,11);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IyIkJlEiIiQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L325" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The kinetic energy is not diagonal, but symmetric!</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L365" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Nb:=10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjTmJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEjMTBGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9Rjk=">IiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L369" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
</Input>
</Group>
<Group labelreference="L319" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">HM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
</Input>
</Group>
<Group labelreference="L340" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">OM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">for m from 1 to Nb do: for n from 1 to m do: VM[m,n]:=VME(m,n): OM[m,n]:=OL(m,n): od: od:</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">#print(map(evalf,VM));</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">for m from 1 to Nb do: for n from 1 to m do: HM[m,n]:=evalf(VM[m,n])+evalf(TME(m,n)): od: od:</Text-field>
</Input>
</Group>
<Group labelreference="L382" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L350" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">E10:=(convert(sort(Re(Eigenvalues(HM,OM))),list));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NywkITMqKio0L3ZzeCk0NSEjPCQhM3c+dFBqTCM0J1whIz0kITMsXUdXXktQTkBGKCQhMyIqNHAmbzQqKltJJyEjPiQhM0hJNnMjSDoncCkpISNAJCIzKikqXGEkeWhDSFhGLSQiMygpelBGLE1LXjhGKCQiMykpNDZAeCN6SkMlRigkIjMtIT11XE0iR0U+RiUkIjMkKio0KCpbeSIqeT4iISM7</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L449" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Nb:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjTmJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEjMjBGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9Rjk=">IiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L450" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
</Input>
</Group>
<Group labelreference="L447" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">HM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
</Input>
</Group>
<Group labelreference="L446" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">OM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">for m from 1 to Nb do: for n from 1 to m do: VM[m,n]:=VME(m,n): OM[m,n]:=OL(m,n): od: od:</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">#print(map(evalf,VM));</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">for m from 1 to Nb do: for n from 1 to m do: HM[m,n]:=evalf(VM[m,n])+evalf(TME(m,n)): od: od:</Text-field>
</Input>
</Group>
<Group labelreference="L448" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L451" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">E20:=(convert(sort(Re(Eigenvalues(HM,OM))),list));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NzYkITMoKlI1KlJbeSk0NSEjPCQhMykqZmo4ZngvaFwhIz0kITMuSUFNUHlyTkBGKCQhMzNTaSo0KVFxM2ohIz4kITM1XW11XF0lUnEkISM/JCIzJypmWyQpWyx1eVxGMCQiMyoqZnMlXE5nc24iRi0kIjNIcVsvZz5aJ1wkRi0kIjMkKjRLWTF1O3BnRi0kIjNwPytmJUhDLWcqRi0kIjMtNVxkJ2U9PVciRigkIjMxK1MzYVk2MUBGKCQiMyIqNEUkKSo0QkYvJEYoJCIzN2cpZSU9SEc9V0YoJCIzXUltJkdjaSp6bEYoJCIzLiFSdmE/LChcNUYlJCIzJypwOl1YMjcwPkYlJCIzQyEpUS84Y0BtU0YlJCIzM11IYDU/VCEzIiEjOyQiMy1dejJPMnlMW0ZN</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L444" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># We see that the first 4 negative-E eigenvalues are confirmed in their lower significant digits.</Text-field>
</Input>
</Group>
<Group labelreference="L445" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Problem 10.8 in Quantum Mechanics by Ghatak and Lokanathan, QC174.12 G485 2004 asks to transform the SE for the s-states of an exp. potential to the Bessel equation.</Text-field>
</Input>
</Group>
<Group labelreference="L362" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># The exact s-state eigenvalues are obtained from:</Text-field>
</Input>
</Group>
<Group labelreference="L389" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">g:=sqrt(r0^2*abs(8*V0));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUTAxNi4wMDAwMDAwMDAwMDBGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9Rjk=">JCIvKysrKysrOyEjNw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L431" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">plot(BesselJ(nu,g),nu=0..30);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="980" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">NiYtJSdDVVJWRVNHNiQ3XXM3JCQiIiEhIiIkIS9qJClSMioqWzwhIzk3JCQiLERjJ3lNOyEjNiQhLyczXS8iW1w5ISM5NyQkIitESmRwSyEjNSQhLy9CbkRRZTUhIzk3JCQiLUQxaydwMyUhIzckIS9OYm5HbW0kKSEjOjckJCIsdm9mViFcISM2JCEvRiI+VSlbQmchIzo3JCQiLXZvSHZAZCEjNyQhLyR6XyYzYSNmJCEjOjckJCIqRFkiUmwhIiokIS8uYTc5I0c2IiEjOjckJCIudm9IbDoneiEjOCQiLzdqJm96RD8kISM6NyQkIi12VlYpUlEqISM3JCIvQTx5eEpZdCEjOjckJCIvRDFSLmshMyIhIzgkIi9ELTh5Mzg2ISM5NyQkIi12VkEpR0EiISM2JCIvdGlkWC9SOSEjOTckJCIvdj1VIltHUSIhIzgkIi88NWBjI2ZzIiEjOTckJCIuRDEvOUdhIiEjNyQiLiNSJj5sWSI+ISM4NyQkIi9RJSkqKXB6QTshIzgkIi8vYGo+S3A+ISM5NyQkIi9EMVIqekZxIiEjOCQiL1wqUUc7bio+ISM5NyQkIi89bjg5eFU8ISM4JCIvKFxDZFMsKyMhIzk3JCQiLzdHKSlHdyN5IiEjOCQiLyIqcHZzdCcqPiEjOTckJCIvMSpHT2FGIz0hIzgkIi89TTI3YicpPiEjOTckJCIsdiRldWk9ISM1JCIvWnRTKlwncD4hIzk3JCQiLXYkNHNQLSMhIzYkIi8nM1A0KHpOPSEjOTckJCIqTil6JT0jISIpJCIvIiopPmFGVWciISM5NyQkIi1EMVkjZU0jISM2JCItZiU0JTQqRyIhIzc3JCQiLEQnMyZvXSMhIzUkIi8pNC9xI3AlMyohIzo3JCQiL0QxKnk2cm0jISM4JCIvLSEpKipbMWBbISM6NyQkIi5EY3JzdCNHISM3JCIvW3JRNXUwUyEjOzckJCIvdj1VT2ooKUghIzgkIS9sY3VYKXovJSEjOjckJCItdm9YKnk5JCEjNiQhLyQzdSNIaHYjKSEjOjckJCIsRCdwWidIJCEjNSQhL1R4VkNTIz0iISM5NyQkIi1EYyRmXVckISM2JCEvPWE4M0soWyIhIzk3JCQiKnZUT2YkISIpJCEvYmlkbSg0dCIhIzk3JCQiLXZWVEFVUCEjNiQhLyU0Rz5bWyE+ISM5NyQkIit2JFsiPlEhIiokIS9uXCplOWInPiEjOTckJCItRDFFMicqUSEjNiQhL0RKIWY+YisjISM5NyQkIix2JG8qSChSISM1JCEvbzheR2xDPyEjOTckJCItdm81IypcUyEjNiQhL0tPYlgjSC0jISM5NyQkIi1ESiZwUD8lISM2JCEvTndpOip6Jj4hIzk3JCQiLXYkKnpoZFYhIzYkIS8lPikqKT0mXCI9ISM5NyQkIi12JEhHbl4lISM2JCEuV2o5WURmIiEjODckJCItdiRmUWVuJSEjNiQhL0hfOnY3MDghIzk3JCQiLXYkKilbXCRbISM2JCEvWCcpcEssZScqISM6NyQkIi12JD5mUypcISM2JCEvVSE9RGFJKmUhIzo3JCQiK0QjZkU6JiEiKiQhLz4xKVJfaCM+ISM6NyQkIi1EYyNmN0omISM2JCIvPngkZlZqNCMhIzo3JCQiLHZHZilwYSEjNSQiLiNbeEJKP2chIzk3JCQiLXY9JGYlR2MhIzYkIi93TSlSODdxKiEjOjckJCIvREpYKilmInomISM4JCIvQFhMUXI0OCEjOTckJCIudj1kUVomZiEjNyQiL2ZlanB4KGYiISM5NyQkIi92Vik+eXk2JyEjOCQiL3ApUWcnb0M9ISM5NyQkIitEeSwiRychIiokIi8kbzNOKVwkKT4hIzk3JCQiL3YkNGNrR04nISM4JCIvUCcqUW1tST8hIzk3JCQiLnZvSDZaVSchIzckIi9GPVhBZ2o/ISM5NyQkIi9EIkcuZWxcJyEjOCQiL2whZU9FQTMjISM5NyQkIi12b1pTb2whIzYkIi9APUU8YyczIyEjOTckJCIuPm44R1ZnJyEjNyQiLz0hNEgwTTMjISM5NyQkIi92by86RFNtISM4JCIuQG9xSG4yIyEjODckJCIuY0UoWzx3bSEjNyQiLyNmWilcY20/ISM5NyQkIi5EMUMpNDduISM3JCIvendIbyVIMCMhIzk3JCQiL0Rjd1wlUnknISM4JCIvVk5lMV86PyEjOTckJCIsRHIiemJvISM1JCIvWSFlO1hbJz4hIzk3JCQiLkQiR2xiPHEhIzckIi90S0t2JFshPSEjOTckJCItdlY4S3pyISM2JCIvOWwlcGxwZSIhIzk3JCQiLnYkZmgzVHQhIzckIi9iJzNgJWU+OCEjOTckJCIrdjQmR10oISIqJCIvaztxVUU3NSEjOTckJCIsRCwhR2x3ISM1JCIvKCoqUlIzKFJuISM6NyQkIiowNHgjeSEiKSQiL3J4J2ZxJm9KISM6NyQkIix2M1EsKnohIzUkIS8iUXgib2MvWyEjOzckJCIrRHJjXyIpISIqJCEvQnM2diIqKjQlISM6NyQkIil3NDQkKSEiKCQhL0VEaGUvbHUhIzo3JCQiK3YhR2NZKSEiKiQhL1lZcyQ+RDEiISM5NyQkIipiZUBpKSEiKSQhL20rdDRrXTghIzk3JCQiK0QhKm95KCkhIiokIS9wKHlaVVhnIiEjOTckJCIudiRmJHlIMSohIzckIS8oKjNwND1pPiEjOTckJCItdiRwbnNNKiEjNiQhLzJRRyk0LDwjISM5NyQkIi5jRWR6PFYqISM3JCEvKFFjIltqLEEhIzk3JCQiL0RjXjlIOyYqISM4JCEvbnpybkA+QSEjOTckJCIucC9MLjNnKiEjNyQhL1RqXiRwSEEjISM5NyQkIi52JDRfSiZvKiEjNyQhLz0iPTwkNDhBISM5NyQkIi92PW4qUVYmKSohIzgkIS4iR0A4bWBAISM4NyQkIixERk9CKyIhIiokIS94J1xjbFMvIyEjOTckJCItREpMKDQuIiEjNSQhL0RONDAwYzwhIzk3JCQiKlI1J2Y1ISIoJCEvJFI7Nmk8TyIhIzk3JCQiL1FmVmlFdzUhIzckIS5AQG47XjQiISM4NyQkIi92PSg0QUg0IiEjNyQhLyVSWiQpPWEzKSEjOjckJCIvN3ldemQ0NiEjNyQhLik9SzNEIjMmISM5NyQkIi52ViFRQkU2ISM2JCEvSkdvQzApKj4hIzo3JCQiLzcuZHEoNDkiISM3JCIvTCwpejddXighIzs3JCQiL3ZvNC5zYjYhIzckIi8pKVtXdHAiWyQhIzo3JCQiL1FNaU5ZcTYhIzckIi95cmJlXGVoISM6NyQkIis6bz8mPSIhIikkIi8kNFI0QjV2KSEjOjckJCIvUSUpKlwjUSw3ISM3JCIvJVEjeikqZlk2ISM5NyQkIi92byU9ZXZAIiEjNyQiL2FYWlNgLDkhIzk3JCQiLzdgcFF0TDchIzckIi9LPkx0SlA7ISM5NyQkIi52VmI0Klw3ISM2JCIvdV9oIikqPSY9ISM5NyQkIi12M2RyIUciISM1JCIvSFxELSRvPiMhIzk3JCQiLkRKJz1fNjghIzYkIi87PS44MGFDISM5NyQkIi92VmBbbVY4ISM3JCIvKj0wKHkvSEUhIzk3JCQiLXZWeSFlUCIhIzUkIi88J3AiKXlTciMhIzk3JCQiL2Neb3I9JFEiISM3JCIvQCE9VUw9cyMhIzk3JCQiLzdHJFxtMFIiISM3JCIvN0skKkhaREYhIzk3JCQiL28vPWUlelIiISM3JCIvUSJlKj05REYhIzk3JCQiL0QiRzlEYFMiISM3JCItOlkqKik0cyMhIzc3JCQiL1FNI3okMz85ISM3JCIvT3NfXSU9cSMhIzk3JCQiLnY9V1VbViIhIzYkIi9iKXkpXEpwRSEjOTckJCIvRGNPM29tOSEjNyQiL2A8KHl1KGZEISM5NyQkIi1ESiM+JilcIiEjNSQiL1dxdydIdFMjISM5NyQkIi52JD46bWs6ISM2JCIuayUpZl52KyMhIzg3JCQiLkRjZFFBaSIhIzYkIi9cPTh0NEc7ISM5NyQkIi12dExVJW8iISM1JCIvRCQpKUdjJVI3ISM5NyQkIitiam1bPCEiKSQiL281SlJBUyopISM6NyQkIi12eWJeNj0hIzUkIi9ASHQoWzpDJyEjOjckJCIudlZWREIoPSEjNiQiLzdtI3A7M0UlISM6NyQkIi1ENlclKVI+ISM1JCIuUl1NdycqbyMhIzk3JCQiKzpLXis/ISIpJCIvPT9xJCk9RTwhIzo3JCQiLEQ2IUhsPyEiKiQiL0pURnAhUi8iISM6NyQkIi52JDR3KVI3IyEjNiQiL3pEJHoxbVgnISM7NyQkIix2WmYiKT0jISIqJCIvb2swRmtBUCEjOzckJCIudlY/UyZbQSEjNiQiLypIZTxMbzsjISM7NyQkIi52PVliO0ojISM2JCIvLExQSTAuNyEjOzckJCIsRDtpTFAjISIqJCIvMS5oKnBTaSchIzw3JCQiLnYkZkwnelYjISM2JCIvRVpvYD9xTSEjPDckJCIqKj49K0QhIigkIi80bSlcKWZDPSEjPDckJCItREUmNFFjIyEjNSQiLyJcKUhFU3EjKiEjPTckJCIudlY+NXBpIyEjNiQiL19iLDVoWlkhIz03JCQiK2JKKltvIyEiKSQiL3cjMydcI1xVIyEjPTckJCItRHIiWzh2IyEjNSQiL2ZucT9pSDYhIz03JCQiKkwneTVHISIoJCIvaDV0QFU4YyEjPjckJCIudlYhKWZUKEchIzYkIi9FajVdXz9FISM+NyQkIi5EY0k7WyRIISM2JCIvInp3eDNcQyIhIz43JCQiJCskISIiJCIvd0lrJ1FfXSYhIz8tJSZDT0xPUkc2JiUkUkdCRyQiIzUhIiIkIiIhISIiJCIiISEiIi0lJVZJRVdHNiQ7JCIiISEiIiQiJCskISIiJShERUZBVUxURy0lK0FYRVNMQUJFTFNHNictSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1UScmIzk1Nzs2Ii8lJ2ZhbWlseUdRITYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJmZhbHNlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiJRITYiLSUlRk9OVEc2JSUoREVGQVVMVEclKERFRkFVTFRHIiM1JStIT1JJWk9OVEFMRyUrSE9SSVpPTlRBTEctJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiQhZiEiIi0lKUJPVU5EU19ZRzYjJCIjXSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJSE0KiEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiUhKVEhIiItJSlDSElMRFJFTkc2Ig==</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L464" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Five bound states exist in this case: the roots wrt nu are to be found:</Text-field>
</Input>
</Group>
<Group labelreference="L385" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">nu0:=fsolve(BesselJ(nu,g),nu=4..5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUknZnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiUtSShCZXNzZWxKR0YkNiRJI251R0YnJCIvKysrKysrOyEjN0YsOyIiJSIiJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L386" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">E0:=-nu0^2/(8.)/r0^2; # this is the energy for given nu.</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJC1JJ2Zzb2x2ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlLUkoQmVzc2VsSkdGJjYkSSNudUdGKSQiLysrKysrKzshIzdGLjsiIiUiIiYiIiMkIS8rKysrXTd5ISM7</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L438" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">nu1:=fsolve(BesselJ(nu,g),nu=1.5..2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUknZnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiUtSShCZXNzZWxKR0YkNiRJI251R0YnJCIvKysrKysrOyEjN0YsOyQiIzohIiIiIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L437" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">E1:=-evalf(nu1^2/(8.)/r0^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJC1JJ2Zzb2x2ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlLUkoQmVzc2VsSkdGJjYkSSNudUdGKSQiLysrKysrKzshIzdGLjskIiM6ISIiIiIjRjYkIS8rKysrXTd5ISM7</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L462" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">nu2:=fsolve(BesselJ(nu,g),nu=5..6);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEoJiM5NTc7MkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUTA1LjIyODQ5NzcxNDM1MTdGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9Rjk=">JCIvPE45eFxHXyEjOA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L463" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">E2:=-evalf(nu2^2/(8.)/r0^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">JCEvVHdSeXJOQCEjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L466" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">nu3:=fsolve(BesselJ(nu,g),nu=2..4);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEoJiM5NTc7M0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUTAyLjg0MTY3OTI1OTE1MjRGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9Rjk=">JCIvQzpmI3o7JUchIzg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L465" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">E3:=-evalf(nu3^2/(8.)/r0^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">JCEvWGE6UnEzaiEjOg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L468" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">nu4:=fsolve(BesselJ(nu,g),nu=0.5..1.5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEoJiM5NTc7NEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUTEwLjY5MDQxNzU1NjUxMDIwRidGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5">JCIvPzVsYjwvcCEjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L467" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">E4:=-evalf(nu4^2/(8.)/r0^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">JCEvPkUkUk1TcyQhIzs=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L459" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L461" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># We can study systematically for each of the 5 eigenvalues how well the numerical calculation is doing.</Text-field>
</Input>
</Group>
<Group labelreference="L460" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L390" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># We optimize the calculation wrt the basis parameter.</Text-field>
</Input>
</Group>
<Group labelreference="L391" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">phi:=n->uL(n,0,1.0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkjdUxHRiU2JTkkIiIhJCIjNSEiIkYlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L404" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag:=proc(Nb,beta,N_E) local phi,VME,TME,OL,VM,HM,OM,m,n,res; phi:=n->uL(n,0,beta);</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VME:=(m,n)->int(phi(n)*V*phi(m),r=0..infinity); TME:=(m,n)->-1/2*int(phi(n)*diff(phi(m),r$2),r=0..infinity); OL:=(m,n)->int(phi(n)*phi(m),r=0..infinity);</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">HM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">OM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">for m from 1 to Nb do: for n from 1 to m do: VM[m,n]:=VME(m,n): OM[m,n]:=OL(m,n): od: od:</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">for m from 1 to Nb do: for n from 1 to m do: HM[m,n]:=evalf(VM[m,n])+evalf(TME(m,n)): od: od:</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">res:=(convert(sort(Re(Eigenvalues(HM,OM))),list)); [seq(res[j],j=1..N_E)];</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">end:</Text-field>
</Input>
</Group>
<Group labelreference="L402" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L395" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(5,1,5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyckITMhKipHKFItP08vNSEjPCQhMz5nd0JxYlpMWiEjPSQhMyYqcC4kZiswIVw8RigkITNHIVtGJD5ONmhQISM+JCIzOCFSUyhRMHdeXEYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L396" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(5,1/2,5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyckITNxUlZZIj1WaCEqKiEjPSQhMyIpSE82LiZlWkUlRiUkITMxU3M7ckopPkEiRiUkITMpKnB1YzMoUkZUIiEjPiQiMyUpcCJ5QCYpPSEzRyEjPw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L469" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># A smaller beta-value results in worse (higher) energies for all states, except the last one (which is still coming out as unbound). Note this 5-by-5 calculation has only 5 eigenvalues!</Text-field>
</Input>
</Group>
<Group labelreference="L470" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">j:=4; # pick the state for which the analysis is carried out:</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiakYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSI0RidGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5">IiIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L397" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">LL5:=[]: for i from 1 to 20 do: beta:=3/10*i; LL5:=[op(LL5),[beta,Diag(5,beta,5)[j]]]: od:</Text-field>
</Input>
</Group>
<Group labelreference="L405" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">PL1:=plot(LL5): beta:='beta': PL0:=plot(E||(j-1),beta=0..2,color=green): plots[display](PL0,PL1,view=[0..2,-0.1..0.2]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="756" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L406" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">j;# </Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L407" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">#LL5;</Text-field>
</Input>
</Group>
<Group labelreference="L408" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Exercise: find the minimum value from the 5-by-5 calculation by optimizing wrt beta; how big is the relative error?</Text-field>
</Input>
</Group>
<Group labelreference="L471" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Try 10-by-10 calculations:</Text-field>
</Input>
</Group>
<Group labelreference="L414" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">LL10:=[]: for i from 1 to 5 do: beta:=1+1/10*i; LL10:=[op(LL10),[beta,Diag(10,beta,5)[j]]]: od:</Text-field>
</Input>
</Group>
<Group labelreference="L412" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">PL2:=plot(LL10,color=blue,style=point,symbol=cross): plots[display](PL0,PL1,PL2,view=[0..2,-0.065..-0.035]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="944" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L413" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L409" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># we see that the 10-by-10 diagonalization is less sensitive to the basis parameter beta.</Text-field>
</Input>
</Group>
<Group labelreference="L410" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Exercise: track the relative error (compared to the exact answer) as a function of beta.</Text-field>
</Input>
</Group>
<Group labelreference="L427" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L411" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Now ask the questions: is there a bound state in the L=1 sector (p-wave)?</Text-field>
</Input>
</Group>
<Group labelreference="L415" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L422" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag:=proc(Nb,beta,L,N_E) local phi,VME,TME,OL,VM,HM,OM,m,n,res; phi:=n->uL(n,L,beta);</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VME:=(m,n)->int(phi(n)*(V+L*(L+1)/2/r^2)*phi(m),r=0..infinity); TME:=(m,n)->-1/2*int(phi(n)*diff(phi(m),r$2),r=0..infinity); OL:=(m,n)->int(phi(n)*phi(m),r=0..infinity);</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">VM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">HM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">OM:=Matrix(Nb,Nb,shape=symmetric):</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">for m from 1 to Nb do: for n from 1 to m do: VM[m,n]:=VME(m,n): OM[m,n]:=OL(m,n): od: od:</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal">for m from 1 to Nb do: for n from 1 to m do: HM[m,n]:=evalf(VM[m,n])+evalf(TME(m,n)): od: od:</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">res:=(convert(sort(Re(Eigenvalues(HM,OM))),list)); [seq(res[j],j=1..N_E)];</Text-field>
</Input>
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">end:</Text-field>
</Input>
</Group>
<Group labelreference="L416" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L417" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(5,1,1,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyMkITNsUkhZKHB6ISlmJyEjPQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L418" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(5,2,1,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEzKikqXGlIVlhObCchIz0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L419" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(5,3,1,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEzJSpSb104LS9hbSEjPQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L420" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(5,4,1,3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyUkITNUU0FwaUU0Vm0hIz0kITM1NXg6YTlkVj5GJSQiM19IaSp6OyxALSlGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L452" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(10,4,1,3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyUkITNNZ0w8RUYvYW0hIz0kITNGU1ApKXpqNSY0JEYlJCEzTj5meTFLWiZlKSEjPg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L453" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(20,4,1,3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyUkITNwPnZgdUYvYW0hIz0kITN5PmY3LF8zKDQkRiUkITMrK3RaQjM7NTZGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L454" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(30,4,1,4);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyYkITNwUkFkdUYvYW0hIz0kITMkKkgibzg/JjMoNCRGJSQhMzAhKTRGPTlANTZGJSQhMy4hWyVvUDhUIXAiISM+</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L455" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(30,5,1,5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyckITNvejg1dUYvYW0hIz0kITNDPz8+LF8zKDQkRiUkITMwUyNlJmUlNC02IkYlJCEzKikqZTMqNCdIJiplIiEjPiQiM0tdWi1fNTJCTkYs</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L456" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(30,3,1,5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyckITNJSTRrdUYvYW0hIz0kITMyPyNlNz8mMyg0JEYlJCEzJSpmXCM9VTYtNiJGJSQhMykqKkg9ckVtLXEiISM+JCIzRCFlIW88XXJRbiEjPw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L457" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Diag(30,2,1,5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyckITNCNU5ddUYvYW0hIz0kITMjKSoqPkosXzMoNCRGJSQhMyw/dyU9VTYtNiJGJSQhMzs1cXB6Q1crPCEjPiQiMy0/aUAoSCpcN0QhIz8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L458" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L472" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># For L>0 we do not have an exact result to compare against. Thus, we need to be diligent when determining the best results from matrix diagonalization.</Text-field>
</Input>
</Group>
<Group labelreference="L473" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>