Exact solutions for quantum mechanical particle with spin 1 in the external homogeneous magnetic field

TL;DR

This paper derives exact solutions for a spin-1 quantum particle in a homogeneous magnetic field using the Petiau-Duffin-Kemmer formalism, providing explicit energy level formulas for different solution types.

Contribution

It introduces a comprehensive method to obtain exact solutions for spin-1 particles in magnetic fields within a covariant formalism, expanding analytical tools in quantum mechanics.

Findings

Three independent solution types identified

Explicit energy level formulas derived for each solution type

Method demonstrates the utility of the Petiau-Duffin-Kemmer formalism

Abstract

With the use of the general covariant matrix 10-dimensional Petiau -- Duffin -- Kemmer formalism in cylindrical coordinates and tetrad there are constructed exact solutions of the quantum-mechanical equation for a particle with spin 1 in presence of an external homogeneous magnetic field. There are separated three linearly independent types of solutions; in each case the formula for energy levels has been found.