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Homework Help: Time-dependent perturbation theory

  1. Dec 28, 2007 #1
    [SOLVED] time-dependent perturbation theory

    1. The problem statement, all variables and given/known data
    My book uses time-dependent perturbation theory to derive the following expression for the transition of \psi_{100} to \psi_{210} in the hydrogen atom in a uniform magnetic field with magnitude [tex]\mathcal{E}[/tex]

    [tex] \frac{131072}{59049} \frac{e^2 \mathcal{E}^2 a_o^2}{(E_2 -E_1)^2} \sin^2(\frac{E_2-E_1}{2 \hbar}t) [/tex]

    What I don't understand is why you cannot just increase [tex]\mathcal{E}[/tex] until the probability goes above 1?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 28, 2007 #2


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    Science Advisor
    Homework Helper

    Because it's 'perturbation theory'. If the field becomes large, then whole approximation that the field can be treated as a 'perturbation' goes out the window and the formula is invalid.
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