Time-dependent Dunkl-Pauli Oscillator

TL;DR

This paper investigates the dynamics of a time-dependent Dunkl-Pauli oscillator in two dimensions, deriving exact solutions and analyzing the effects of Dunkl operators on quantum states with time-varying parameters.

Contribution

It introduces a Hamiltonian for the time-dependent Dunkl-Pauli oscillator, providing exact eigenvalues and eigenfunctions using the Lewis-Riesenfeld method, and explores the impact of Dunkl operators on quantum systems.

Findings

Derived exact eigenvalues and eigenfunctions for the system.

Analyzed the influence of Dunkl operators on quantum phases.

Provided explicit expressions for wave functions and energy levels.

Abstract

This study explores the time-dependent Dunkl-Pauli oscillator in two dimensions. We constructed the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and frequency, initially in Cartesian coordinates. Subsequently, we reformulated the Hamiltonian in polar coordinates and analyzed the eigenvalues and eigenfunctions of the Dunkl angular operator, deriving exact solutions using the Lewis-Riesenfeld invariant method. Our findings regarding the total quantum phase factor and wave functions reveal the significant impact of Dunkl operators on quantum systems, providing precise expressions for wave functions and energy eigenvalues. This work enhances the understanding of quantum systems with deformed symmetries and suggests avenues for future research in quantum mechanics and mathematical physics.