Quantum mechanics for a vector particle in the magnetic field on 4-dimensional sphere

Abstract

Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential equations in the variable r are solved in hypergeometric functions. T he study o f z-dependence of the wave function has been reduced to a system of three linked ordinary differential 2-nd order equations; till now the system in z variable is not solved.

27 pages; Nauchno-Technicheskie Vedomosti. Saint Petersburg State Polytechnical University