Some problem with for loop not giving results

Questions
, ,
1

nm = 100;
Reap[For[v2 = -10., v2 < -9, v2 = v2 + 1/10.,
v[x_] := Ix^3 + Iv2x^2;
c[m_, n_] := 1./Sqrt[2^(m + n)Factorial[m]Factorial[n]Pi];
x1[m_,
n_] := (1/Sqrt[2.])(Sqrt[n + 1]KroneckerDelta[m, n + 1] +
Sqrt[n]KroneckerDelta[m, n - 1]);
g[m_, n_] :=
c[m, n]Integrate[
Exp[-x^2]HermiteH[m, x]x^3HermiteH[n, x], {x, -Infinity,
Infinity}];
p2[m_,
n_] := .5(2n + 1)KroneckerDelta[m, n] - .5Sqrt[n(n - 1)]
KroneckerDelta[m, n - 2] - .5Sqrt[(n + 1)(n + 2)]
KroneckerDelta[m, n + 2];
x3[m_,
n_] := (1/
Sqrt[8.])(Sqrt[(n + 1.)(n + 2)(n + 3)]
KroneckerDelta[m, n + 3.] +
Sqrt[n*(n - 1)(n - 2)]
KroneckerDelta[m, n - 3] + (3*(n + 1)Sqrt[n + 1])
KroneckerDelta[m, n + 1] +
3nSqrt[n]KroneckerDelta[m, n - 1]);
h[m_, n_] := p2[m, n] + Ix3[m, n] + Iv2x[m, n];
mat = Table[h[m, n], {m, 0, nm}, {n, 0, nm}];
Eigenvalues[mat];
a = Sort[Re[Select[Eigenvalues[mat], Abs[Im[#]] < 10^-5 &]]];
j = Length[a];
b = a[[1 ;; 7]];
Sow[Join[{v2, Part[b, 1]}]]]][[2, 1]]

2

suggest you use Table instead of For and define the functions first before calling Table.

3

Probably the problem is that you are using x[m,n] instead of x1[m,n]:
nm = 100;
Reap[For[v2 = -10., v2 < -9, v2 = v2 + 1/10.,
v[x_] := Ix^3 + Iv2x^2;
c[m_, n_] := 1./Sqrt[2^(m + n)Factorial[m]Factorial[n]Pi];
x1[m_, n_] := (1/Sqrt[2.])(Sqrt[n + 1]KroneckerDelta[m, n + 1] +
Sqrt[n]KroneckerDelta[m, n - 1]);
g[m_, n_] :=
c[m, n]Integrate[
Exp[-x^2]HermiteH[m, x]x^3HermiteH[n, x], {x, -Infinity,
Infinity}];
p2[m_, n_] := .5(2n + 1)KroneckerDelta[m, n] - .5
Sqrt[n(n - 1)]KroneckerDelta[m, n - 2] - .5
Sqrt[(n + 1)(n + 2)]KroneckerDelta[m, n + 2];
x3[m_, n_] := (1/
Sqrt[8.])(Sqrt[(n + 1.)(n + 2)(n + 3)]
KroneckerDelta[m, n + 3.] +
Sqrt[n*(n - 1)(n - 2)]
KroneckerDelta[m, n - 3] + (3*(n + 1)Sqrt[n + 1])
KroneckerDelta[m, n + 1] +
3nSqrt[n]KroneckerDelta[m, n - 1]);
h[m_, n_] := p2[m, n] + Ix3[m, n] + Iv2x1[m, n];
mat = Table[h[m, n], {m, 0, nm}, {n, 0, nm}]; Eigenvalues[mat];
a = Sort[Re[Select[Eigenvalues[mat], Abs[Im[#]] < 10^-5 &]]];
j = Length[a]; b = a[[1 ;; 7]]; Sow[Join[{v2, Part[b, 1]}]]]][[2,
1]]

I even better would write it as:

nm = 100;
c[m_, n_] := 1./Sqrt[2^(m + n)Factorial[m]Factorial[n]Pi];
x1[m_, n_] := (1/Sqrt[2.])(Sqrt[n + 1]KroneckerDelta[m, n + 1] +
Sqrt[n]KroneckerDelta[m, n - 1]);
g[m_, n_] :=
c[m, n]Integrate[
Exp[-x^2]HermiteH[m, x]x^3HermiteH[n, x], {x, -Infinity,
Infinity}];
p2[m_, n_] := .5(2n + 1)KroneckerDelta[m, n] - .5Sqrt[n(n - 1)]
KroneckerDelta[m, n - 2] - .5Sqrt[(n + 1)(n + 2)]*
KroneckerDelta[m, n + 2];
x3[m_, n_] := (1/
Sqrt[8.])(Sqrt[(n + 1.)(n + 2)(n + 3)]
KroneckerDelta[m, n + 3.] +
Sqrt[n*(n - 1)(n - 2)]
KroneckerDelta[m, n - 3] + (3*(n + 1)Sqrt[n + 1])
KroneckerDelta[m, n + 1] + 3nSqrt[n]*KroneckerDelta[m, n - 1]);

Reap[For[v2 = -10., v2 < -9, v2 = v2 + 1/10.,
v[x_] := Ix^3 + Iv2x^2;
h[m_, n_] := p2[m, n] + Ix3[m, n] + Iv2x1[m, n];
mat = Table[h[m, n], {m, 0, nm}, {n, 0, nm}]; Eigenvalues[mat];
a = Sort[Re[Select[Eigenvalues[mat], Abs[Im[#]] < 10^-5 &]]];
j = Length[a]; b = a[[1 ;; 7]];

Sow[Join[{v2, Part[b, 1]}]]]][[2, 1]]