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Homework Help: Energy shift using perturbation theory

  1. Mar 30, 2010 #1
    1. The problem statement, all variables and given/known data
    I am looking at the relativistic correction to the kinetic energy for a hydrogen atom. I am told that the perturbation is usually written as
    H = -p^4/(8 m^3 c^2)
    and need to find the energy shift

    2. Relevant equations
    I know that from the perturbation theory the energy shift is given by
    delta E = <n|H|n>

    From the unperturbed hamiltonian
    p^2 / (2m) = En - V
    so we can rewrite the perturbation in terms of En and V

    The part I am not sure about is how to approach the wavefunctions n? Normally we have to solve an integral....what do I use as wavefunctions????

  2. jcsd
  3. Mar 30, 2010 #2


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    Science Advisor

    You want to take the matrix element of the perturbation over unperturbed wave functions. The unperturbed wave functions are the hydrogen atom wave functions without the perturbation. You can look them up on Wikipedia or Google them. So to find the energy shift of the ground state, for example, you need to apply the perturbation to the unperturbed ground state, then multiply be the complex conjugate of the unperturbed ground state, and integrate the result over all space. Does this answer your question?
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