A/S Wavefunction calcs: more

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1518] A/S Wavefunction calcs: more
• From: P.Jemmer at sussex.ac.uk (Patrick Jemmer)
• Date: Wed, 21 Jun 1995 21:24:09 -0400
• Organization: University of Sussex

```HellO; since my last post, I have tackled this problem some more
myself, and have come up with the following:

--------------------------------------
g[a__] := Module[{perms = Permutations[{a}], sigs, len},
sigs = Map[Signature, perms];
len = Length[sigs];
Sum[sigs[[j]]*f[Apply[Sequence, perms[[j]]]], {j, len}]];

aswf:=g[q1,q2,q3];

b[i_,j_]:=1-e*2*a[i,j];
bb:=b[q1,q2]*b[q1,q3]*b[q2,q3];

ex:=((Series[bb//Expand,{e,0,10}]//Normal)/. e->1);

ovlp:=f[q1,q2,q3]*ex*aswf//Expand;

ovlpbs:=ovlp/. f[w_,x_,y_]->c1[w]*c2[x]*v3[y];

sbs1:={Integrate[c1[b_]*c1[b_],b_]->1,\
Integrate[c2[b_]*c2[b_],b_]->1,\
Integrate[v3[b_]*v3[b_],b_]->1,\
Integrate[v4[b_]*v4[b_],b_]->1,\
Integrate[c1[b_]*v3[b_],b_]->0,\
Integrate[c2[b_]*v3[b_],b_]->0,\
Integrate[c1[b_]*c2[b_],b_]->0,\
Integrate[c1[b_]*v4[b_],b_]->0,\
Integrate[c2[b_]*v4[b_],b_]->0,\
Integrate[v3[b_]*v4[b_],b_]->0};

intfn1[q_]:=Integrate[q,q1];
intfn2[q_]:=Integrate[q,q2];
intfn3[q_]:=Integrate[q,q3];

ovllst=Table[ovlpbs[[i]],{i,1,Length[ovlpbs]}];

ovlpint1:=ovlpintc/.sbs1;
ovlpint2:=Sum[ovlpint1[[i]],{i,1,Length[ovlpint1]}];

kl=ovlpint2//.Integrate[a1_,b1_]->a1

Definition[kl]>>klfile
--------------------------------------

[Q]: I would like to combibe the a[i,j] together with the
various {c1[a], c2[b],....} to give the bra-kets for example:

< c1[a] c2[b] | a[a,b] | c2[a] c1[b] >

in some kind of notation (symbolic only). I seem to
get stuck because some terms get represented by

Power[c1[c],2], for example.

Thanks!

Patrick.

```

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