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Homework Help: 1st-order WF correction

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data

    A have a bit of a general question regarding 1st order wave function corrections using perturbation theory.

    In a problem like the infinite potential well where you have states numbered like n = 1, 2, 3, ..., how do you compute the sum for the 1st order correction when you have infinite terms?:

    [tex]\psi_n^{(1)} = \Sigma_{l \ne n} \frac{<\psi_n^{(0)}|H'|\psi_l^{(0)}>}{E_n^{(0)} - E_l^{(0)}} \psi_l^{(0)}[/tex]

    I guess I don't know how to get <n|H'|l> so I can evaluate the sum
     
    Last edited: Sep 18, 2010
  2. jcsd
  3. Sep 19, 2010 #2

    kuruman

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    Do you know what your perturbation H' looks like? Sometimes the non-zero terms in the summation result in something that can be summed analytically.
     
  4. Sep 20, 2010 #3
    This was the thinking I was missing!

    So for H' = constant there is no first-order correction because [itex]l \ne n[/itex], yes?
     
  5. Sep 20, 2010 #4

    kuruman

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    Correct. If you add a constant to your Hamiltonian, you shift the zero of energy but you do not change its eigenstates.
     
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