# Having difficulties using results returned by Solve

I'm new to Mathematica, and I am still having some issues figuring out the general syntax. I've got to use Mathematica, as my research requires a powerful symbolic math program.

I'm having trouble taking values from Solve and plugging them back into functions. My code is below. I would ultimately like to be able to take the values from solve, and plug them back into psi_n+1 and E_n+1, and make these values become the new psi_n and E_n, and do this iteratively in a for loop.

ClearAll["Global*"]
ℏ = 1;
m = 1;
L = 1;
Subscript[ψ, n][x_] = x (L - x);
g[x_] = x;
H[f_, x_] := (-ℏ^2/(2 m)) D[f, {x, 2}];
a[x_] = H[Subscript[ψ, n][x], x];

Subscript[E, n] =
Integrate[Conjugate[Subscript[ψ, n][x]] g[x] a[x], {x, 0, L}] /
Integrate[Conjugate[Subscript[ψ, n][x]] Subscript[ψ, n][x], {x, 0,L}];

Subscript[ψ, n + 1][x_, C1_, C0_] :=
Subscript[ψ, n][x] + g[x] (C1/C0) (a[x] - Subscript[E, n] Subscript[ψ, n][x]);

Subscript[E, n + 1][C1_, C0_] =
Integrate[
Conjugate[Subscript[ψ, n + 1][x, C1, C0]] g[x]
H[Subscript[ψ, n + 1][x, C1, C0], x],
{x, 0, L}] /
Integrate[
Conjugate[Subscript[ψ, n + 1][x, C1, C0]] Subscript[ψ, n + 1][x, C1, C0],
{x, 0, L}];

b[x_] = Subscript[E, n] Subscript[ψ, n][x];
c[x_, C1_, C0_] = Subscript[E, n + 1][C1, C0] Subscript[ψ, n][x];
e[x_] = a[x] - b[x];
f[x_, C1_, C0_] = a[x] - c[x, C1, C0];

eqn1[C0_, C1_] =
C0 Integrate[Conjugate[Subscript[ψ, n][x]] f[x, C1, C0], {x, 0, L}] +
C1 Integrate[
Conjugate[Subscript[ψ, n][x]]
(H[g[x] e[x], x] - Subscript[E, n + 1][C] g[x] e[x]),
{x, 0, L}];

eqn2[C0_, C1_] =
C0 Integrate[
Conjugate[Subscript[ψ, n][x]] H[g[x] f[x, C1, C0], x] -
Subscript[E, n + 1][C1, C0] g[x] f[x, C1, C0],
{x, 0, L}] +
C1 Integrate[
Conjugate[Subscript[ψ, n][x]]
(H[g[x](H[g[x] e[x], x] - Subscript[E, n + 1][C1, C0] g[x] e[x]), x] -
Subscript[E, n] g[x] (H[g[x] e[x], x] -
Subscript[E, n + 1][C1, C0] g[x] e[x])),
{x, 0, L}];

Solve[eqn1[C0, C1] == 0 && eqn1[C0, C1] == 0, {C1, C0}, Reals]

• Please see this post on copying readable code from MMA to this site. You will also want to try reducing your code to a minimal working example. – MarcoB Mar 19 '19 at 4:13
• Please be aware of the fact that is is dangerous to use subscripted variables in Mma. They often work as expected, but may sometimes suddenly bring an error, where you do not expect. Consider instead of Subscript[a,n] to use a[n]`. – Alexei Boulbitch Mar 19 '19 at 8:11