Time-Dependent Dunkl-Schr\"odinger Equation with an Angular-Dependent Potential

TL;DR

This paper derives exact solutions for a time-dependent Schrödinger equation involving a harmonic oscillator with angular-dependent potential using Dunkl derivatives and Lewis-Riesenfeld invariants, expanding quantum analysis methods.

Contribution

It introduces a novel analytical approach combining Dunkl derivatives and Lewis-Riesenfeld invariants for time-dependent quantum systems with angular potentials.

Findings

Exact solutions for the time-dependent Dunkl-Schrödinger equation

Extension of quantum analysis to angular-dependent potentials

New insights into dynamic quantum systems with varying parameters

Abstract

In this manuscript, we investigate the analytical solution of the time-dependent Schr\"odinger equation for a harmonic oscillator with time-dependent mass and frequency, coupled with angular-dependent potential energy by utilizing the Dunkl derivatives. To obtain the solution, we employ the Lewis-Riesenfeld invariant methodology. Our approach broadens the scope of quantum mechanical analyses, offering exact solutions and new insights into dynamic quantum systems under varying conditions.