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Stark Effect using first order variation theory.

  1. Jul 6, 2008 #1
    EDIT: Sorry... I have to use perturbation theory. My mistake.

    Hey... I have a quick question. I have to calculate the approximate change in energy via variation theory when the 'error' Hamiltonian for the Stark effect is defined as: [tex]|\vec{E}|cos\theta\bullet eR[/tex]

    If I'm not mistaken, the change in energy of the 1s orbital of a hydrogen atom will be:

    <E>=k[tex]\int r^3e^{-2r/a}dr \int sin\theta cos\theta d\theta \int d\varphi[/tex]

    However, the middle integral becomes 0 when the limits of 0 and pi are plugged in. This doesn't seem right. Am I doing anything incorrectly?
  2. jcsd
  3. Jul 6, 2008 #2
    The perturbation couples 1s with 2p state. It would not perturb the 1s only (In this case your integral is correct). Besides your volume element in r should be r^2 and not r^3.

  4. Jul 7, 2008 #3
    One "r" comes from the definition of the perturbed Hamiltonian. The other two come from the jacobian in spherical coordinates.

    I'm not really sure what I have to do now, though. I'm not familiar with your notation. Sorry =(
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