Particle with spin 1 in a magnetic field on the spherical plane S_{2}

TL;DR

This paper derives exact solutions for a spin-1 particle in a magnetic field on a spherical surface, providing a generalized energy level formula and solving both nonrelativistic and relativistic equations.

Contribution

It presents the first exact solutions for a spin-1 particle in a magnetic field on a curved spherical surface, including a generalized energy quantization formula.

Findings

Exact solutions for spin-1 particle in spherical magnetic field

Generalized energy level formula derived

Both nonrelativistic and relativistic equations solved

Abstract

There are constructed exact solutions of the quantum-mechanical equation for a spin S=1 particle in 2-dimensional Riemannian space of constant positive curvature, spherical plane, in presence of an external magnetic field, analogue of the homogeneous magnetic field in the Minkowski space. A generalized formula for energy levels describing quantization of the motion of the vector particle in magnetic field on the 2-dimensional space S_{2} has been found, nonrelativistic and relativistic equations have been solved.