A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics

TL;DR

This paper develops an analytical path integral approach for time-dependent Dunkl quantum systems, deriving explicit propagators and wave functions for models with varying mass and potentials, thus expanding Dunkl operator applications in quantum dynamics.

Contribution

It introduces a novel path integral formalism for time-dependent Dunkl quantum mechanics using generalized canonical transformations, enabling explicit solutions for complex systems.

Findings

Derived exact propagators for Dunkl-harmonic oscillator with time-dependent parameters

Extended Dunkl operator methods to time-dependent quantum systems

Provided analytical solutions for models with pulsating mass

Abstract

This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By employing generalized canonical transformations, we reformulated the path integral to develop an explicit expression for the propagator. This formalism is applied to specific cases, including a Dunkl-harmonic oscillator with time-dependent mass and frequency. Solutions for the Dunkl-Caldirola-Kanai oscillator and a model with a strongly pulsating mass are derived, providing exact propagator expressions and corresponding wave functions. These findings extend the utility of Dunkl operators in quantum mechanics, offering new insights into the dynamics of time-dependent quantum systems.