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Expectation values

  1. Oct 2, 2009 #1
    I'm trying to check that the expectation value <E> is E for the wavefunction

    sqrt(2/L) sin(2pix / L)

    I know the shortcut way of doing it by saying that the hamiltonian multiplied by the function is just the eigenvalue E multiplied by the function, and since the function is normalized the answer is E. However, I want to try to check it:

    But when I take the hamiltonian of the function (V=0) and then multiply that by the complex conjugate and integrate from 0 to L I get

    2 h^2 / mL^2

    which is not quite what I would expect if it equals E since I know for the 1D Schrodinger equation

    E_n = n^2 h^2 / 8mL^2
    =>E_2 = h^2 / 2mL^2

    What's wrong?
  2. jcsd
  3. Oct 2, 2009 #2


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    Homework Helper
    Gold Member

    You must be integrating incorrectly, if you show your calculations, we can point out your error...
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