Time-dependent perturbation theory

  • Thread starter ehrenfest
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[SOLVED] time-dependent perturbation theory

Homework Statement


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?

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
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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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