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Cosine perturbation to potential well

  1. May 7, 2014 #1
    1. The problem statement, all variables and given/known data

    10h626v.png

    Part (b): Find the perturbed energy.

    2. Relevant equations



    3. The attempt at a solution

    I've solved everything, except part (b).
    I got an answer of 0 for part (b) for all orders, which is kind of strange, as one would expect some perturbation.

    [tex]\Delta E_n = \langle \psi_n |U|\psi_n\rangle[/tex]
    [tex]= \frac{2}{L}U_0\int_0^L cos(\frac{2\pi}{L}x)sin^2(\frac{n\pi x}{L}) [/tex]
    [tex] = 0 [/tex]

    Integrating this leads to zero.

    All the other orders give zero as well.
     
    Last edited: May 7, 2014
  2. jcsd
  3. May 9, 2014 #2
    I'm thinking since the period is L, integrating a function throughout its entire period gives 0 area?
     
  4. May 10, 2014 #3

    BruceW

    User Avatar
    Homework Helper

    not generally. for example, think of the function cos(x)+5, the curve lies above the x axis for all values of x, so it definitely does not integrate to zero. Anyway, you should try to do the integration for the three values of ##n## and see what you get.
     
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