Dunkl-Schr\"odinger equation with time-dependent harmonic oscillator potential

TL;DR

This paper derives explicit wavefunctions for one- and three-dimensional Dunkl Schrödinger equations with time-dependent harmonic oscillator potentials, using the Lewis-Riesenfeld method, highlighting parity-dependent invariants.

Contribution

It introduces a novel approach to solving Dunkl Schrödinger equations with time-dependent potentials by applying the Lewis-Riesenfeld method, including explicit wavefunction forms.

Findings

Explicit wavefunctions for Dunkl harmonic oscillators derived

Parity-dependent invariants identified and characterized

Method applicable to time-dependent quantum systems with Dunkl derivatives

Abstract

In this paper, using the Lewis-Riesenfeld method, we determine the explicit form of the wavefunctions of one- and three-dimensional harmonic oscillators with time-dependent mass and frequency within the framework of the Dunkl derivative, which leads to the derivation of a parity-dependent of the invariant and auxiliary equation.