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## Homework Statement

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)

ans =

x^2*(-1/2*cos(x)*sin(x)+1/2*x)-1/2*x*cos(x)^2+1/4*cos(x)*sin(x)+1/4*x-1/3*x^3

(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.

stephen