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samee
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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=p2/2m
Sin=sqrt(2/L)cos(npix/L)
En=n2pi2hbar2/2mL2
V(x)=kx2/2
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 En(1) by taking;
En1=<n|H|n>
=<n|V|n>
=V * integral(2/Lcos2(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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