Pauli Oscillator In Noncommutative Space

TL;DR

This paper explores the quantum behavior and thermodynamics of a Pauli oscillator in noncommutative space, revealing how deformation parameters and magnetic fields influence energy spectra and thermodynamic properties.

Contribution

It derives the wave functions, energy spectrum, and thermodynamic functions of the Pauli oscillator in noncommutative space, including critical deformation and magnetic field values.

Findings

Deformation parameter must be smaller than 2.57×10^{-26} m^2.

Magnetic field effects alter thermodynamic functions.

Noncommutative space modifies Zeeman effect and thermodynamics.

Abstract

In this study, we investigate the Pauli oscillator in a noncommutative space. In other words, we derive wave function and energy spectrum of a spin half non-relativistic charged particle that is moving under a constant magnetic field with an oscillator potential in noncommutative space. We obtain critical values of the deformation parameter and the magnetic field, which counteract the normal and anomalous Zeeman effects. Moreover, we find that the deformation parameter has to be smaller than $2.57\times 10^{-26}m^2$. Then, we derive the Helmholtz free energy, internal energy, specific heat, and entropy functions of the Pauli oscillator in the noncommutative space. With graphical methods, at first, we compare these functions with the ordinary ones, and then, we demonstrate the effects of magnetic field on these thermodynamic functions in the commutative and noncommutative space, respectively