Exactly solvable problems for a 2-particle system with a homogeneous relative space

Abstract

The Schrödinger equation that admits the freedom to choose the transitivity group of the relative space of a 2-particle system is considered. With the help of dynamic symmetry considerations, potentials that provide exact solutions of this equation are found. The explicit form of these solutions for both continuous and discrete energy spectra is obtained and the physical aspects of these solutions are discussed.