Dunkl-Pauli Equation in the Presence of a Magnetic Field

TL;DR

This paper analytically solves the Dunkl-Pauli equation for a spin-1/2 particle in a magnetic field, revealing parity-dependent dynamics and exploring thermal properties in equilibrium.

Contribution

It introduces the Dunkl derivative into the Pauli equation, leading to parity-dependent solutions and a detailed analysis of thermal quantities.

Findings

Derived analytical solutions showing parity dependence

Analyzed thermal properties of the system in equilibrium

Revealed effects of Dunkl derivative on quantum dynamics

Abstract

The Pauli equation, an important equation of quantum mechanics, allows us to study the dynamics of spin-$1/2$ particles. The Dunkl derivative, when used instead of the ordinary derivative, leads to obtaining parity-dependent solutions. Motivated by these facts, in this work, we consider a two-dimensional nonrelativistic spin-$1/2$ particle system in the presence of an external magnetic field, and we investigate its parity-dependent dynamics by solving the Pauli equation analytically. Next, we assume the system to be in thermal equilibrium, and we examine various thermal quantities of the system.