Phy5646/An Example of spontaneous emission calculation

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(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,