Nonrelativistic system of interacting particles in the model of the noncommutative operators of coordinates and momenta of different particles

Abstract

It is shown that the Schr\"{o}dinger equation for a system of interacting particles whose Compton wavelengths are of the same order of magnitude as the system size is contradictory and is not strictly nonrelativistic, because it is based on the implicit assumption that the velocity of propagation of interactions is finite. In the framework of the model of the noncommutative operators of coordinates and momenta of different particles, the equation for a wave function which has no above-mentioned drawbacks is deduced. The significant differences from solutions of the nonrelativistic Schr\"{o}dinger equation for large values of the interaction constant are found, and the comparison of analogous results for hydrogenlike atoms with experimental data is carried out.