Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation-Reference-Cited by-同舟云学术

Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation

Published:2022-11-10 Issue:33n34 Volume:37 Page:
ISSN:0217-7323
Container-title:Modern Physics Letters A
language:en
Short-container-title:Mod. Phys. Lett. A

Author:

Mota R. D.¹,Ojeda-Guillén D.²

Affiliation:

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

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

Abstract

In this paper, we introduce a generalization of the Dunkl derivative with two parameters to study the Schrödinger equation in Cartesian and polar coordinates in two dimensions. The eigenfunctions and the energy spectrum for the harmonic oscillator and the Coulomb problem are derived in an analytical way and it is shown that our results are properly reduced to those previously reported for the Dunkl derivative with a single parameter.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217732322502248

Reference35 articles.

1. Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?

2. A Note on the Quantum Rule of the Harmonic Oscillator

3. Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems

4. Common algebraic structure for the Calogero - Sutherland models

5. Exact operator solution of the Calogero-Sutherland model

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