Nonrelativistic Approximation for Quasi-Planes Wave of a Spin 1 Particle in Lobachevsky Space

Abstract

Spin 1 particle in Pauli approximation is investigated on the background of a curved space of constant negative curvature, Lobachevsky space. Nonrelativistic approximation is performed in the system of 10 equations resulted from separating the variables in Duffin–Kemmer equation specified in quasi-cartesian coordinates. The problem is solved exactly in Bessel functions, the quantum states are determined by four quantum numbers. The treatment is substantially based on the use of a generalized helicity operator in Lobachevsky space model.