The Schrödinger equation for N-particle system with homogeneous relative space

Abstract

The Schrödinger equation for a closed system of N ≥ 2 particles, the relative space of which can be a homogeneous space of any of groups isomorphic to E(3N - 3), SO (3N - 2) or SO (3N - 3,1), is formulated. The formulation is given in termins of variables subordinated to special transformational laws under Galilean transformations of physical space by use of the group representations theory allowing to construct dynamics of particles directly at a quantum level.