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## Homework Statement

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?

## Homework 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

## 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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