Dunkl-Klein-Gordon equation in higher dimensions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F25%3A50022492" target="_blank" >RIV/62690094:18470/25:50022492 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S0217732325500944" target="_blank" >http://dx.doi.org/10.1142/S0217732325500944</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0217732325500944" target="_blank" >10.1142/S0217732325500944</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dunkl-Klein-Gordon equation in higher dimensions

Popis výsledku v původním jazyce

In this study, we replace the standard partial derivatives in the Klein-Gordon equation with Dunkl derivatives and obtain exact analytical solutions for the eigenvalues and eigenfunctions of the Dunkl-Klein-Gordon equation in higher dimensions. We apply this formalism to two key quantum mechanical systems: the d-dimensional harmonic oscillator and the Coulomb potential. First, we introduce Dunkl quantum mechanics in d-dimensional hyperspherical coordinates, followed by an analysis of the d-dimensional Dunkl-Klein-Gordon oscillator. Subsequently, we derive the energy spectrum and eigenfunctions, which are expressed using confluent hypergeometric functions. Furthermore, we examine the impact of the Dunkl formalism on both the eigenvalues and eigenfunctions. In the second case, we explore both the bound-state solutions and scattering scenarios of the Dunkl-Klein-Gordon equation with the Coulomb potential. The bound-state solutions are represented in terms of confluent hypergeometric functions, while the scattering states enable us to compute the particle creation density and probability using the Bogoliubov transformation method.

Název v anglickém jazyce

Dunkl-Klein-Gordon equation in higher dimensions

Popis výsledku anglicky

In this study, we replace the standard partial derivatives in the Klein-Gordon equation with Dunkl derivatives and obtain exact analytical solutions for the eigenvalues and eigenfunctions of the Dunkl-Klein-Gordon equation in higher dimensions. We apply this formalism to two key quantum mechanical systems: the d-dimensional harmonic oscillator and the Coulomb potential. First, we introduce Dunkl quantum mechanics in d-dimensional hyperspherical coordinates, followed by an analysis of the d-dimensional Dunkl-Klein-Gordon oscillator. Subsequently, we derive the energy spectrum and eigenfunctions, which are expressed using confluent hypergeometric functions. Furthermore, we examine the impact of the Dunkl formalism on both the eigenvalues and eigenfunctions. In the second case, we explore both the bound-state solutions and scattering scenarios of the Dunkl-Klein-Gordon equation with the Coulomb potential. The bound-state solutions are represented in terms of confluent hypergeometric functions, while the scattering states enable us to compute the particle creation density and probability using the Bogoliubov transformation method.

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

2025

Kód důvěrnosti údajů

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

Název periodika

Modern Physics Letters A

ISSN

0217-7323

e-ISSN

1793-6632

Svazek periodika

40

Číslo periodika v rámci svazku

25

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

22

Strana od-do

"Article number: 2550094"

Kód UT WoS článku

001497458100001

EID výsledku v databázi Scopus

2-s2.0-105006633313