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<Group labelreference="L1" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">restart; Digits:=14:</Text-field>
</Input>
</Group>
<Group labelreference="L2" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Completeness Relation - how much is complete?</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># we look at a subset of states -> how much do they contribute towards unity in add(|n><n|, n=1..N)?</Text-field>
</Input>
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<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># How do we approach the question?</Text-field>
</Input>
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<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># think about powers of operators -> take their matrix representation, compare that against direct calculations.</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Use A=-I*d/dx, and A^2=-d/dx^2 as an operator example, and a subset of the harmonic oscillator states.</Text-field>
</Input>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">with(orthopoly);</Text-field>
</Input>
<Output>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">w:=0.75;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEid0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSUwLjc1RidGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5">JCIjdiEiIw==</Equation></Text-field>
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<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">alpha:=sqrt(w);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIzo9RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkktSSNtbkdGJDYkUTEwLjg2NjAyNTQwMzc4NDQ0RidGMi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGMUYy">JCIvVyV5LmEtbSkhIzk=</Equation></Text-field>
</Output>
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<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">phi:=n->exp(-0.5*(alpha*x)^2)*H(n,alpha*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSRleHBHRiU2IywkKiYkIiImISIiIiIiKiZJJmFscGhhR0YlIiIjSSJ4R0YlRjVGMkYxRjItSSJIR0YlNiQ5JComRjRGMkY2RjJGMkYlRiVGJQ==</Equation></Text-field>
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<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">NI:=n->int(phi(n)^2,x=-infinity..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkaW50R0YlNiQqJC1JJHBoaUdGJTYjOSQiIiMvSSJ4R0YlOywkSSlpbmZpbml0eUclKnByb3RlY3RlZEchIiJGNkYlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">NI(0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIvSSplVGBtLyMhIzg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">NT:=[seq(1/sqrt(NI(n)),n=0..99)]:</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Now we have to pick some states |mu> and |nu>, which will be used to define the A^2 matrix element.</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># For simplicity we will choose as reference states harmonic oscillator eigenstates with some other oscillator constant:</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">beta:=0.5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIzo9RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkktSSNtbkdGJDYkUSQwLjVGJ0YyLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0YxRjI=">JCIiJiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">psi:=n->exp(-0.5*(beta*x)^2)*H(n,beta*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkKiYkIiImISIiIiIiKiZJJWJldGFHRiUiIiNJInhHRiVGOEY1RjRGNS1JIkhHRiU2JDkkKiZGN0Y1RjlGNUY1RiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">NIb:=n->int(psi(n)^2,x=-infinity..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJC1JJHBzaUdGJTYjOSQiIiMvSSJ4R0YlOywkSSlpbmZpbml0eUdGLCEiIkY5RiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">n1:=0: n2:=2:</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">NC1:=1/sqrt(NIb(n1));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkTkMxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRMTAuNTMxMTI1OTY2MDEzNjFGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9Rjk=">JCIvaDhnJ2Y3SiYhIzk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">NC2:=1/sqrt(NIb(n2));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkTkMyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRMTAuMTg3NzgxMzg2MTE2MjRGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9Rjk=">JCIvQztoUSJ5KD0hIzk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME:=-NC1*NC2*int(psi(n1)*diff(psi(n2),x$2),x=-infinity..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">JCEvaydIJnB3bjwhIzk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Now let us see how we get this by inserting a completeness relation (however, a truncated one!)</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># WE COMPUTE THE FIRST ME by ACTING with -I*diff on the bra, so we change it to +I*diff !</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME1:=n->I*NC1*NT[n+1]*int(phi(n)*diff(psi(n1),x),x=-infinity..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKipeIyIiIkYrSSROQzFHRiVGKyZJI05UR0YlNiMsJjkkRitGK0YrRistSSRpbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JComLUkkcGhpR0YlNiNGMUYrLUklZGlmZkdGNTYkLUkkcHNpR0YlNiNJI24xR0YlSSJ4R0YlRisvRkM7LCRJKWluZmluaXR5R0Y1ISIiRkdGK0YlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME1(0); # derivative of an even function is odd !</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEjMC5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZHLUYsNiRRIklGJ0YvRi8=">XiMkIiIhIiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME1(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiM2Ji1JI21uR0YkNiRRMTAuMjg0OTM4MzgyMTE5MzVGJ0YvLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRJjAuMGVtRicvRkVGUC1GSTYkUSJJRidGL0YvLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y0Ri8=">XiMkIS9OPkBRUVxHISM5</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME2:=n->-I*NC2*NT[n+1]*int(phi(n)*diff(psi(n2),x),x=-infinity..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkTUUyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYoLUYsNiVRIm5GJ0YvRjItRjY2LVEoJiM4NTk0O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZYLUYjNictRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmpuLUYjNiotSSNtbkdGJDYkUSJJRidGOS1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIRldGWS1GLDYlUSROQzJGJ0YvRjJGYm8tSSVtc3ViR0YkNiUtRiw2JVEjTlRGJ0YvRjItRiM2Ji1GIzYmRlEtRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSEZpbkZbby1GX282JFEiMUYnRjlGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGYm8tSShtZmVuY2VkR0YkNiQtRiM2Ki1JKG1zdWJzdXBHRiQ2Jy1GNjYtUSgmIzg3NDc7RidGOUY7Rj5GQEZCRkRGRkZIRldGWS1GIzYnRmZuLUYsNiVRKCYjODczNDtGJ0YvRjJGaHBGW3FGOUZdci8lMXN1cGVyc2NyaXB0c2hpZnRHUSIyRidGXXEtRiM2Ji1GIzYoLUYsNiVRJyYjOTY2O0YnL0YwRj1GOS1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGV0ZZLUZhcTYkLUYjNiZGUUZocEZbcUY5RjlGaHBGW3FGOUZiby1GYXE2JC1GIzYoLUkmbWZyYWNHRiQ2KC1GIzYmLUY2Ni1RKyZQYXJ0aWFsRDtGJ0Y5RjtGPkZARkJGREZGRkhGV0ZZRmhwRltxRjktRiM2Ji1GIzYnRlt0LUYsNiVRInhGJ0YvRjJGaHBGW3FGOUZocEZbcUY5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZqdC8lKWJldmVsbGVkR0Y9RmJvLUYjNigtRiw2JVEnJiM5Njg7RidGanJGOUZbcy1GYXE2JC1GIzYmLUYsNiVRI24yRidGL0YyRmhwRltxRjlGOUZocEZbcUY5RmhwRltxRjlGOUY5LUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjNlbUYnLyUmZGVwdGhHRmB2LyUqbGluZWJyZWFrR1ElYXV0b0YnLUY2Ni1RMCZEaWZmZXJlbnRpYWxEO0YnRjlGO0Y+RkBGQkZERkZGSEZXRllGYnRGaHBGW3FGOUY5RjlGaHBGW3FGOUZocEZbcUY5RmhwRltxRjk=">Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKipeIyEiIiIiIkkkTkMyR0YlRiwmSSNOVEdGJTYjLCY5JEYsRixGLEYsLUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJi1JJHBoaUdGJTYjRjJGLC1JJWRpZmZHRjY2JC1JJHBzaUdGJTYjSSNuMkdGJUkieEdGJUYsL0ZEOywkSSlpbmZpbml0eUdGNkYrRkhGLEYlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME2(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">XiMkIS8/ZnheJz0wKCEjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr:=N->add(ME1(n)*ME2(n),n=0..N);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kiTkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkYWRkRyUqcHJvdGVjdGVkRzYkKiYtSSRNRTFHRiU2I0kibkdGJSIiIi1JJE1FMkdGJUYwRjIvRjE7IiIhOSRGJUYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr(0);</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="L21" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEvb2lhcU00PyEjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr(2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEvb2lhcU00PyEjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr(3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEvIVJvayEqcDYjISM5</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr_T:=[seq(ME_tr(n),n=0..30)]:</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">plot([seq([j-1,ME_tr_T[j]],j=1..31)]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="413" type="two-dimensional" width="874" 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="L36" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr_T[10],ME;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQkIS9dYzROJ1J6IiEjOSQhL2snSCZwd248RiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr_T[20],ME;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQkIS9iYC5EJXl3IiEjOSQhL2snSCZwd248RiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ME_tr_T[30],ME;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQkIS8heSw0bnh3IiEjOSQhL2snSCZwd248RiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Exercises:</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># change the states |mu> and |nu>. For example: decrease their beta, so that they are more delocalized. Then repeat the convergence analysis.</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">#</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># Change the states |mu> and |nu> by choosing different n1 and n2, then repeat the convergence analysis.</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"># This is sending the message: a truncated completeness relation -> there is no universal statement possible as to what happens when N is xx or yy.</Text-field>
</Input>
</Group>
</Worksheet>