# Cosine perturbation to potential well

1. May 7, 2014

### unscientific

1. The problem statement, all variables and given/known data

Part (b): Find the perturbed energy.

2. Relevant equations

3. The attempt at a solution

I've solved everything, except part (b).
I got an answer of 0 for part (b) for all orders, which is kind of strange, as one would expect some perturbation.

$$\Delta E_n = \langle \psi_n |U|\psi_n\rangle$$
$$= \frac{2}{L}U_0\int_0^L cos(\frac{2\pi}{L}x)sin^2(\frac{n\pi x}{L})$$
$$= 0$$

All the other orders give zero as well.

Last edited: May 7, 2014
2. May 9, 2014

### unscientific

I'm thinking since the period is L, integrating a function throughout its entire period gives 0 area?

3. May 10, 2014

### BruceW

not generally. for example, think of the function cos(x)+5, the curve lies above the x axis for all values of x, so it definitely does not integrate to zero. Anyway, you should try to do the integration for the three values of $n$ and see what you get.