Problems of quantum theory in the light of the theory of perturbations

Abstract

1. It is shown in the following paper that the physical purport of Delannay's method in the theory of perturbations consists in successive approximation of a given motion by means of a set of conditionally periodic motions. 2. It is further shown, that at every degree of approximation two possible cases must be taken into account. In the one the motion of the system is periodic with respect to a certain variable, in the other this variable performs a libration. 3. In both cases formulæ for carrying through the calculations are given, fit for the purposes of the theory of quanta. 4. A modification of Delaunay's method, due to Whittaker is applicable to one of the two cases only and is therefore incomplete. 5. Delaunay's method (in our modification) quite automatically yields at every degree of approximation the special coördinates, looked for in the theory of quanta.

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