# Simple time-independent perturbation problem. QM

1. Nov 15, 2008

### armis

1. The problem statement, all variables and given/known data
"Suppose we put a delta-function in the center of the infinite square well:
$${H^{'}} = \alpha\delta(x-a/2)$$ where a is a constant. Find the first order correction to the allowed energies. Explain why the energies are not peturbed for even n"

2. Relevant equations

3. The attempt at a solution

Just to make sure. The energies for even n are not peturbed because the wave functions are odd with respect to the center of the well, thus equal to zero at those points where the delta-function potential is (if our square well is from 0 to a). Is that correct?

2. Nov 15, 2008

### Avodyne

Yes, that's correct!

3. Nov 16, 2008

thanks