On a dynamical quantization

Abstract

A concept of a noncanonical quantization, called dynamical quantization, is defined in an axiomatic way. A dynamical quantization of a system of two nonrelativistic point particles interacting via a harmonic potential is considered in more details. The quantized system exhibits some new features. In particular, it has finite space dimensions. The distance between the particles is preserved in time and can have at most four different values. The position of any one of them cannot be localized, since the operators of the coordinates do not commute. The particles are smeared with a certain probability within a finite volume, which moves together with their centre of mass. The orbital momentum of the composite system is either one or zero.