Tough Perturbation Question (At least for me)

[Ed Quanta]

Consider a particle confined in a two dimensional square well with faces at x=0,a;y=0,a. The doubly degenerate eigenstates appear as Psinp=(2/a)sin(n(pi)x/a)sin(p(pi)x/a)
Enp=E1(n^2 + p^2)

What do these energies become under perturbation H'=10^-3E1sin((pi)x/a)?

Help anyone? No idea how to solve this.

 

[dextercioby]

There's not too much advice to give,just apply the theory strictly.Identify the basis,compute the pertubation matrix and then write the system of equations.

Daniel.

 

[quantumdude]

I agree, this is about as plug-and-chug as it gets. Ed, have you read the relevant material in your textbook? This is a straightforward exercise in time-independent degenerate perturbation theory.

edit:

Here's a nice summary:
http://electron6.phys.utk.edu/qm2/modules/m8/degenerate.htm