Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F24%3A50022145" target="_blank" >RIV/62690094:18470/24:50022145 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10773-024-05862-x" target="_blank" >https://doi.org/10.1007/s10773-024-05862-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10773-024-05862-x" target="_blank" >10.1007/s10773-024-05862-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions

Popis výsledku v původním jazyce

The recent generalization of the Dunkl operator, incorporating six parameters, offers a refined approach to bridging theoretical models and experimental observations. In this study, we apply the fully generalized Dunkl derivatives to solve two cornerstone quantum mechanical problems-the harmonic oscillator and the Coulomb potential-in the non-relativistic context. Our analysis begins with the systems formulated in two-dimensional Cartesian coordinates, followed by a transition to polar coordinates to achieve angular solutions. For the radial component, we identify a required constraint that reduces the set of Wigner parameters by one. This leads to the determination of the radial eigenfunctions and the corresponding energy spectra for both systems, all within the non-relativistic context. Our analysis reveals that the Wigner parameters significantly influence the probability densities, altering the localization of the particle within the potential and highlighting the role of parity in shaping the radial distribution.

Název v anglickém jazyce

Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions

Popis výsledku anglicky

The recent generalization of the Dunkl operator, incorporating six parameters, offers a refined approach to bridging theoretical models and experimental observations. In this study, we apply the fully generalized Dunkl derivatives to solve two cornerstone quantum mechanical problems-the harmonic oscillator and the Coulomb potential-in the non-relativistic context. Our analysis begins with the systems formulated in two-dimensional Cartesian coordinates, followed by a transition to polar coordinates to achieve angular solutions. For the radial component, we identify a required constraint that reduces the set of Wigner parameters by one. This leads to the determination of the radial eigenfunctions and the corresponding energy spectra for both systems, all within the non-relativistic context. Our analysis reveals that the Wigner parameters significantly influence the probability densities, altering the localization of the particle within the potential and highlighting the role of parity in shaping the radial distribution.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10303 - Particles and field physics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

1572-9575

Svazek periodika

63

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

"Article Number: 323"

Kód UT WoS článku

001382306400003

EID výsledku v databázi Scopus

2-s2.0-85212930428