How Do You Calculate First Order Correction in a Perturbed Infinite Square Well?

[abcs22]

Homework Statement

I have the particle in the infinite square well and need to calculate the first order correction energy and the wave function. L is the width and the potential is:
1/2 mw²x² in the -L/2 < x < L/2
and infinity in x <= -L/2 and x>=L/2

Homework Equations

H'=H-H₀[/B]

The Attempt at a Solution

I have stated that the perturbed Hamiltonian is equal to 1/2 mw²x².
I am confused by the integral itself; I am not sure which boundaries to use. I am assuming that since the potential is infinite in L/2 and -L/2 I am not supposed to use those boundary conditions?

 

[Dr Transport]

if the potential is infinite, then the wave function is zero

 

[abcs22]

Yes, but which boundaries to use then when integrating? Is the perturbed Hamiltonian correct?

 

[Dr Transport]

only integrate where the wave function is non-zero

 

[abcs22]

That is what I'm saying. I don't know how to put boundaries since I can't use -L/2 and L/2. In all the other examples I've had, the <= and >= signs were where the potential isn't infinite, as it is in the general infinite square well problem.

 

[Dr Transport]

the original wave function is valid between $\pm L/2$ so those are the limits of integration.

 

[abcs22]

So, I approach this problem the same, regardless this < sign? It confuses me because it says than when x is + or -L/2, the potential is infinite, hence wave function is zero. How is it right to put those boundaries once the integral is solved?

 

[Dr Transport]

it is a perturbation, it is supposed to be small, if the width of the well is not too large the perturbation at the bottom will only slightly affect the energies and wave functions.