A general theorem on the transition probabilities of a quantum mechanical system with spatial degeneracy

Abstract

In the general case of a quantum mechanical system with a Hamiltonian that is invariant for rotations spatial degeneracy will exist. So the initial state must be characterized except by the energy also by e.g. the magnetic quantum number. Both for emission of light and electrons plus neutrinos (ß-radioactivity) of a quantum mechanical system the following theorem is important: the total transition probability from an initial level with some definite magnetic quantum number mi to every possible final level belonging to one energy does not depend on mi. A simple proof is given for this theorem that embraces the case of forbidden transitions, which case is not covered by the usual proof. In the proof a Gibbs ensemble of quantum mechanical systems is used; the necessary and sufficient conditions for the rotational invariance of such an ensemble are given