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"phi:=n->exp(-0.5*(alpha*x)^2)*H(n,alpha*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"nG6\"F%6$I)operatorGF%I&arrowGF%F%*&-I$ expGF%6#,$*&$\"\"&!\"\"\"\"\"*&)I&alphaGF%\"\"#F2)I\"xGF%F6F2F2F1F2-I \"HGF%6$F$*&F5F2F8F2F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "NI:=n->1/sqrt(int(phi(n)^2,x=-infinity..infinity)); # we could g et this from a formula!" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"nG6\"F %6$I)operatorGF%I&arrowGF%F%*$-I%sqrtG6$%*protectedGI(_syslibGF%6#-I$i ntGF%6$*$)-I$phiGF%F#\"\"#\"\"\"/I\"xGF%;,$I)infinityGF-!\"\"F=F>F%F%F %" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "NI(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"/seS$*)QA%!#9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "N:=40; # choosing a matrix size" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#S" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "NI_tab le:=[seq(NI(j),j=0..N)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " #H(1,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "En_table:=[seq( (n+0.5)*w,n=0..N)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "7K$\"#?!\"#$\"#gF %$\"$+\"F%$\"$S\"F%$\"$!=F%$\"$?#F%$\"$g#F%$\"$+$F%$\"$S$F%$\"$!QF%$\" $?%F%$\"$g%F%$\"$+&F%$\"$S&F%$\"$!eF%$\"$?'F%$\"$g'F%$\"$+(F%$\"$S(F%$ \"$!yF%$\"$?)F%$\"$g)F%$\"$+*F%$\"$S*F%$\"$!)*F%$\"%?5F%$\"%g5F%$\"%+6 F%$\"%S6F%$\"%!=\"F%$\"%?7F%$\"%g7F%$\"%+8F%$\"%S8F%$\"%!Q\"F%$\"%?9F% $\"%g9F%$\"%+:F%$\"%S:F%$\"%!e\"F%$\"%?;F%" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 84 "# the Hamiltonian matrix can be obtained by making \+ use of the H0 eigenvalue problem:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "HM:=Matrix(N+1,N+1,shape=symmetric,datatype=float[8]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "for i from 0 to N do: for j from 0 to i do: if i=j then HM[i+1,j+1]:=En_table[i+1]: else HM [i+1,j+1]:=0: fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 112 " HM[i+1,j+1]: = HM[i+1,j+1]+NI_table[i+1]*NI_table[j+1]*int(phi(i)*(V-0.5*w^2*x^2)*p hi(j),x=-infinity..infinity);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "od: od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 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