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Exact solutions of the Schrödinger equation with Dunkl derivative for the free-particle spherical waves, the pseudo-harmonic oscillator and the Mie-type potential

Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Avenida Santa Ana No. 1000, Col. San Francisco Culhuacán, Del. Coyoacán C.P. 04430, Ciudad de México, Mexico

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and

D. Ojeda-Guillén

Escuela Superior de Cómputo, Instituto Politécnico Nacional, Avenida Juan de Dios Bátiz esq. Avenida Miguel Othón de Mendizábal, Col. Lindavista, Del. Gustavo A. Madero, C. P. 07738, Ciudad de México, Mexico

E-mail Address: dojedag@ipn.mx

Corresponding author.

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https://doi.org/10.1142/S0217732322500067Cited by:20 (Source: Crossref)

Abstract

In this paper, we solve exactly the Schrödinger equation for the free-particle, the pseudo-harmonic oscillator and the Mie-type potential in three dimensions with the Dunkl derivative. The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables. The wave functions and the energy spectrum for these potentials are derived in an analytical way and it is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.

Keywords:

PACS: 02.30.Ik, 02.30.Jr, 03.65.Ge, 03.65.Pm

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