On exact solutions of the Dirac equation in a homogeneous magnetic field in the Riemann spherical space

TL;DR

This paper derives exact solutions for the Dirac equation describing a spin-1/2 particle in a spherical Riemann space with a magnetic field, extending quantum magnetic effects to curved geometries.

Contribution

It provides the first exact solutions of the Dirac equation in a positively curved space with a magnetic field, including a generalized energy level formula.

Findings

Exact solutions for the Dirac equation in Riemann spherical space

Generalized energy quantization formula in curved space

Insights into quantum behavior in curved magnetic fields

Abstract

There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in the space of constant positive curvature, spherical Riemann space, 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 particle in magnetic field on the background of the Riemann space geometry, is obtained.