Exact solutions for a quantum-mechanical particle with spin 1 and additional intrinsic characteristics in a homogeneous magnetic field

TL;DR

This paper derives exact solutions for a spin-1 quantum particle with intrinsic properties in a magnetic field using covariant matrix formalism, revealing energy levels and effects of additional characteristics.

Contribution

It introduces a method to find exact solutions for spin-1 particles with intrinsic properties in magnetic fields using the Petiau-Duffin-Kemmer formalism.

Findings

Exact energy level formulas for spin-1 particles in magnetic fields.

Solutions for particles with additional intrinsic electromagnetic characteristics.

Application of covariant matrix formalism to complex quantum systems.

Abstract

With the use of the general covariant matrix 10-dimensional Petiau-Duffin-Kemmer formalism in cylindrical coordinates exact solutions of the quantum-mechanical equation for a particle with spin 1 in the presence of an external homogeneous magnetic field are constructed. Three linearly independent types of solutions are separated; in each case the formula for the energy levels has been found.Within similar technique for the quantum-mechanical equation for a particle with spin 1 and additional intrinsic electromagnetic characteristics - polarizability, exact solutions are found in the presence of an external homogeneous magnetic field.