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Thanks in advance for any advice.

I'm trying to evaluate whether or not a given wavefunction is a valid solution to the time-dependent schroedinger wave equation, the bottom line being that I want to check that two functions are equal to each other at all points (within a tolerance), and I'm not sure if I'm going about it the right way.

I've defined a function, and then want to evaluate two other functions that act on it, so I have:

Code:

```
(*define wavefunction*)
h = 6.626*10^(-34); w = 10;
psi[x_, t_] := (m*w/Pi/h)^(1/4)*
Exp[(-m*w/2/h)*(x^2 + (a^2)/2*(1 + Exp[-2*I*w*t]) + I*h*t/m -
2*a*x*Exp[-i*w*t])];
(*evaluate hamiltonian operation on psi*)
H = (m/2)*Derivative[2, 0][psi][x, t] + (m/2)*w^2*x^2*psi[x, t];
(*evaluate time-depedence*)
T = I*h*Derivative[0, 1][psi][x, t];
```

My questions are:

1) am I taking the right approach to determining what I want to?

2) If so, how can I check for the equality of these two functions?

For (2), I tried H==T, and it just spit out the functions back, and I tried plotting H and T and showing that they are the same, but I just flatlined on both of them, so I'm not sure if my code is wrong or if those approaches are ineffective.

Thanks again!