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 Schrödinger 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 Schrödinger—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 Schrödinger theory.
Highlights
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 Schrödinger 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 Schrödinger—a partition process of the number N −1 is applied
The first one is to provide an evident simplification of the treatment of the Schrödinger perturbation series for energy, especially at large perturbation order N
Summary
A general idea of the present and former papers by the author [4]-[9] is to point out the time importance in the use of the quantum perturbation theory This theory has been developed [10] simultaneously with the Schrödinger wave-mechanical approach to the quantum systems [11] [12] [13]. The first one—created by assuming a constant nucleus-electron distance in course of the electron motion done, say, along a circle—cannot serve to establish any notion of time because no change of the system can be detected by the observer Another situation is obtained when the distance between two mentioned particles changes systematically, say in effect of a planar motion of the electron along an ellipse.
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