(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle is in a box of length L on x-axis. 0<x<L. What is the first order shift due to V(x) of the wavefunction?

2. Relevant equations

H=p^{2}/2m

Si_{n}=sqrt(2/L)cos(npix/L)

E_{n}=n^{2}pi^{2}hbar^{2}/2mL^{2}

V(x)=kx^{2}/2

3. The attempt at a solution

I'm super confused because the shift in the energy is usually determined by a sum, not an integral. Unless I calculate E_{n}^{(1)}by taking;

E_{n}^{1}=<n|H|n>

=<n|V|n>

=V * integral(2/Lcos^{2}(nxpi/L)dx) with limits 0 to L

Is this the correct way to do this one? I didn't include k very well unless I put it in for V at the end...

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# Homework Help: Shift in energy due to weak interaction

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