Time-dependent Dunkl–Pauli oscillator

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. Additionally, we examine the Dunkl–Caldirola–Kanai oscillator as a specific example of a time-dependent system with deformed symmetries, illustrating the effects of time-dependent mass and damping on wave function evolution. Our findings regarding the total quantum phase factor and wave functions reveal the significant impact of Dunkl operators on quantum systems, yielding precise expressions for both wave functions and energy spectra. This work enhances the understanding of quantum systems with deformed symmetries and suggests avenues for future research in quantum mechanics and mathematical physics.