(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:
The transition rate for
is given by
where
is one of the three
states. In particular, for the hydrogen atom in the first excited state,
where
is the Bohr radius. Therefore,
where
is the fine structure constant. However,
Hence,