Simple time-independent perturbation problem. QM

[armis]

Homework Statement

"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"

Homework Equations

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?

 

[Avodyne]

Yes, that's correct!

 

[armis]

thanks