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

Theoretical physics

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. The separation of the t, r, cp, z variables is performed; differential equations in the r variable are solved in hypergeometric functions. The study of 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 is not solved.