Dunkl-Schrödinger equation in higher dimensions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F25%3A50022180" target="_blank" >RIV/62690094:18470/25:50022180 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1088/1402-4896/ada9b2" target="_blank" >http://dx.doi.org/10.1088/1402-4896/ada9b2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1402-4896/ada9b2" target="_blank" >10.1088/1402-4896/ada9b2</a>

Result language

angličtina

Original language name

Dunkl-Schrödinger equation in higher dimensions

Original language description

This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schrödinger equation in higher dimensions, incorporating the Dunkl operator. Two fundamental quantum mechanical problems are examined in their exact forms: the d-dimensional harmonic oscillator and the Coulomb potential. In order to obtain analytical solutions to these problems, both Cartesian and polar coordinate systems were employed. Firstly, the Dunkl-Schrödinger equation is derived in d-dimensional Cartesian coordinates, and then for the isotropic harmonic potential interaction, its solutions are given. Subsequently, using polar coordinates the angular and radial parts of the Dunkl-Schrödinger equation are obtained. It is demonstrated that the system permits the separation of variables in both coordinate systems, with the resulting separated solutions expressed through Laguerre and Jacobi polynomials. Then, the radial Dunkl-Schrödinger equation is solved using the isotropic harmonic, pseudoharmonic, and Coulomb potentials. The eigenstates and eigenvalues are obtained for each case and the behavior of the energy eigenvalue functions are illustrated graphically with the reduced probability densities.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10303 - Particles and field physics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Physica scripta

ISSN

0031-8949

e-ISSN

1402-4896

Volume of the periodical

100

Issue of the periodical within the volume

3

Country of publishing house

GB - UNITED KINGDOM

Number of pages

13

Pages from-to

" Article number: 035301"

UT code for WoS article

001410391400001

EID of the result in the Scopus database

2-s2.0-85216919185