1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Cosine perturbation to potential well

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


    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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted