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

A particle of mass m in the infinite square well is subjected to the perturbation H'=Vo, 0<x<L/2, H'=0 else.

(a) use first order perturbation theory to calculate the energies of the particle

(b) what are the first order corrected wave functions?

(c) if the particle is an electron, how do the frequencies emitted by the perturbed system compare with those of the unperturbed system?

2. Relevant equations

[tex]E_n^{(1)}=H'_{nn}=<E_n^{(0)}|H'|E_n^{(0)}>[/tex]

[tex]|E_n^{(1)}> = \sum_{m \notequal n} \frac{H_{mn}^'}{E_n^{(0)}-E_m^{(0)}} |E_m^{(0)}>[/tex]

3. The attempt at a solution

I solved part (a) and got an answer of Vo/2..i.e. each energy level is shifted up by this amount.

For part (b), I got that there is no correction to the wavefunctions, since m cannot equal n and

[tex]H'_{mn}=\frac{2V_0}{L} \int_0^{L/2} sin(\frac{n \pi}{L}x)sin(\frac{m \pi}{L}x) dx = \frac{V_0}{2} \delta_{mn}[/tex]

did I do part (b) correctly?

also, part (c) is confusing me..does anyone have any thoughts?

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# Infinite square well perturbation

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