Circular Scale of Time and Construction of the Schrödinger Perturbation Series for Energy Made Simple

Abstract

Physically the examined perturbation problem can be regarded as a set of collision events of a time-independent perturbation potential with a quantum system. As an effect of collisions there is an expected definite change of energy of an initially unperturbed state of the system to some stationary perturbed state. The collision process certainly occupies some intervals of time which, however, do not enter the formalism. A striking property is the result of a choice of the sequence of collisions according to the applied circular scale of time: the scale produces almost automatically the energy terms predicted by the Schr ö dinger perturbation theory which usually is attained in virtue of complicated mathematical transformations. Beyond of the time scale and its rules—strictly connected with the perturbation order N introduced by Schr ö dinger—a partition process of the number N -1 is applied. This process, combined with contractions of the time points on the scale, provides us precisely with the perturbation terms entering the Schr ö dinger theory.