Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10303 - Particles and field physics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Theoretical Physics
ISSN
0020-7748
e-ISSN
1572-9575
Volume of the periodical
63
Issue of the periodical within the volume
12
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
"Article Number: 323"
UT code for WoS article
001382306400003
EID of the result in the Scopus database
2-s2.0-85212930428