A particle is inside of a potential described by:
H = p^2/2m + 1/2kx^2, x between -L/2 and L/2
H = infinity, otherwise.
my task is to compute a first-order approximation to the energies of this potential.
The Attempt at a Solution
I attempted to use first-order perturbation theory, but ran into a couple hitches. The first was that when the SHO force is dominant (for some E > Ec), I have to write the infinite energy barriers as some 'perturbation', which I'm not sure how to do. Another is that when I try to do the expectation value for where the SHO force is a perturbation, (<n|H'|n>, where H' = 1/2kx^2), I get something really complicated and messy:
>> int((x^2)*sin(x)^2, x)
(sans a lot of stuff..)
So there must be something I'm doing wrong. First of all, how can I approximate infinity? Secondly, what am I doing wrong with the other first-order correction (with the SHO energy as the perturbation?) I could really use some hints.
Thanks a lot.