The ground state of a hydrogen atom (n = 1, l = 0) is subjected to a time-dependent potential as follows:

Using time-dependent perturbation theory, obtain an expression for the transition rate at which the electron is emitted with momentum p. Show, in particular, how you may compute the angular distribution of the ejected electron (in terms of θ and ϕ defined with respect to the z-axis). Discuss briefly the similarities and the differences between this problem and the (more realistic) photoelectric effect. If you have a normalization problem, the final wave function may be taken to be

with L very large, but you should be able to show that the observable effects are independent of L.

Transcribed Image Text:

V(x, t) Vocos(kz - wt).