On the Hermitian momentum of Wigner-Dunkl quantum mechanics

¹ Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University - Jinju 660-701, Korea
² European Southern Observatory - Karl-Schwarzschild-Straße 2, 85748 Garching, Germany
³ Research Center for Quantum Physics, Huzhou University - Huzhou 313000, China
⁴ Centro de Investigación en Computación, Instituto Politécnico Nacional - UPALM, CDMX 07738, Mexico
⁵ Faculty of Physics, Shahrood University of Technology - Shahrood, Iran

^(a) E-mail: mimip44@naver.com (corresponding author)
^(b) E-mail: gjunker@eso.org
^(c) E-mail: On leave from IPN due to permission of research stay in China; dongsh2@yahoo.com
^(d) E-mail: h.hasanabadi@shahroodut.ac.ir

Received: 6 November 2022
Accepted: 3 January 2023

Abstract

In this paper the Hermitian momentum operator on the usual Hilbert space is constructed for the Wigner-Dunkl quantum mechanics utilizing a symmetric Dunkl derivative. The inverse of the derivative is shown to exhibit different realization on the subspaces of even and odd functions. The continuity conditions at finite discontinuities of symmetric potential is investigated. As an example, the finite symmetric square well is discussed in detail.