On the quantum dynamics of degenerate systems

Abstract
§1. It is well known that if F i = n i h , i ═ 1, 2, ... (1) be a set of quantum conditions applicable to a class of dynamical systems, then F i must satisfy the definite condition: ∂F i /∂ a ═ 0, (2) where a is a parameter, such as an external field, etc., which is followed to undergo a slow non-systematic variation. In other words, F i must be an “adiabatic invariant” of the class of systems. Burgers has shown, on the basis of Newtonian dynamics, that I i ═ ∫ 0 P i dq i fulfils this condition in the case of a conditionally periodic system of several degrees of freedom where q i p i are separable Hamiltonian co-ordinates, provided the system he non-degenerate, i. e , provided no relation of the form ∑ i s i j ν i = 0 (3) exist between the frequencies ν i , where s i j is an integer, positive or negative, In the case of a system of charged particles, W. Wilson has shown that on the basis of the general theory of relativity, p i should be replaced by π i where π i = p i + e A i , (4)

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