Phy5646/An Example of spontaneous emission calculation

(Submitted by Team 1)

This example was taken from "Theory and Problems of Quantum Mechanics", Yoaf Peleg, et al, p. 298.

Problem: Find the transition rate of spontaneous emission for a hydrogen atom in the first excited state

Solution: (a) To first order we need to calculate ${H}^{'}=q{\mathcal {E}}\langle n|x|n\rangle$. It is easy to show that $\langle n|x|n\rangle =0$. One way is to use the relation