One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
A. Benchikha, B. Hamil, B. C. L\"utf\"uo\u{g}lu, B.Khantoul
TL;DR
This paper develops a path integral approach to one-dimensional Dunkl quantum mechanics, deriving propagators, energy spectra, and wave functions for free particles and harmonic oscillators with Dunkl derivatives.
Contribution
It introduces a novel path integral method for Dunkl quantum mechanics and explicitly calculates propagators and spectra for key systems.
Findings
Derived the propagator for Dunkl free particle and harmonic oscillator
Obtained energy spectra and bound-state wave functions
Validated results through spectral decomposition
Abstract
In the present manuscript, we employ the Feynman path integral method to derive the propagator in one-dimensional Wigner-Dunkl quantum mechanics. To verify our findings we calculate the propagator associated with the free particle and the harmonic oscillator in the presence of the Dunkl derivative. We also deduce the energy spectra and the corresponding bound-state wave functions from the spectral decomposition of the propagator.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Molecular spectroscopy and chirality · Quantum chaos and dynamical systems