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Revista Mexicana de Física

Step potential and Ramsauer-Townsend effect in Wigner-Dunkl quantum mechanics

Ali Askari, HASSAN HASSANABADI, Won Sang Chung

Published Jan 3, 2023• 0 citations
Publisher

Abstract

In this paper the continuity equation for Wigner-Dunkl-Schrodinger equation is studied. Some properties of ¨ ν-deformed functions related to Dunkl derivative are also studied. Based on these, the step potential and Ramsauer-Townsend effect are discussed in Wigner-Dunkl quantum mechanics
DOI
10.31349/revmexfis.69.011201

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The hydrodynamical form of Wigner–Dunkl quantum mechanics has been formulated. The main step to get such formulation was to derive a pair of Madelung-like equations (called Madelung–Wigner–Dunkl equations) from the Schrödinger equation appearing in Wigner–Dunkl quantum mechanics. Some aspects of both equations contained in the pair, i.e. the inhomogeneous continuity equation and the quantum Hamilton–Jacobi equation, have been investigated and discussed. With certain assumption, the relation between the expectation value of the quantum potential appearing in the quantum Hamilton–Jacobi equation and the so-called Fisher information has been derived. Then an uncertainty relation between momentum and position which may be tighter than the standard uncertainty relation has been derived by using Cramér–Rao inequality and Fisher information.
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