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pset3 - PH 216 Problem set 3 Due 4/20 1 Consider the...

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PH 216, Problem set 3, Due 4/20 1. Consider the hydrogen atom in an excited n = 2 state, which is subjected to an external uniform electric field E . Do not neglect the spin of the electron. Assume that the field E is su ciently weak so that eEa 0 is small compared to the fine structure, but such that the “Lamb shift” δ ( δ = 1057 MHz) cannot be neglected. This “Lamb shift” is an e ff ect from QED that breaks the degeneracy between the 2 S 1 / 2 and 2 P 1 / 2 states: if the Lamb-shift is neglected, then the 2 s 1 / 2 and 2 p 1 / 2 states are degenerate with energy, E (0) = 1 2 m e c 2 α 2 5 128 m e c 2 α 4 , as computed in class. Including the Lamb shift, 2 s 1 / 2 and 2 p 1 / 2 are no longer degenerate. Instead, we have E (0) (2 s 1 / 2 ) E (0) (2 p 1 / 2 ) > 0 , which defines . Assume here that the Lamb shift can be included as a term H LS in the unperturbed Hamiltonian. Thus, for present purposes you can treat the problem as a two-level system consisting of the the 2 S 1 / 2 and 2 P 1 / 2 states of hydrogen. In
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