Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.10954 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917206216933376 |
|---|---|
| author | Lobos, Nikko John Leo S. |
| author_facet | Lobos, Nikko John Leo S. |
| contents | We present exact analytical solutions for the radial Dunkl-Schrödinger equation (DSE) confined by the Deng-Fan molecular potential. By employing the Pekeris approximation to resolve the centrifugal singularity and applying the parametric Nikiforov-Uvarov method, we derive closed-form expressions for the energy eigenspectrum and the corresponding radial wavefunctions expressed in terms of Jacobi polynomials. Our investigation reveals that the Dunkl reflection parameter $μ$ fundamentally alters the system's topology by breaking spatial symmetry and introducing a parity-dependent repulsive force. Numerical analysis demonstrates a monotonic increase in energy eigenvalues with increasing $μ$, confirming an effective "hard core" behavior at the origin. The results are shown to be consistent with standard quantum mechanics in the limit $μ\to 0$. This study establishes the Dunkl formalism as a robust tool for modeling quantum systems characterized by parity-dependent exclusion effects and strong short-range correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Analytical Solutions of the Dunkl-Schrödinger Equation for the Deng-Fan Potential Lobos, Nikko John Leo S. Mathematical Physics We present exact analytical solutions for the radial Dunkl-Schrödinger equation (DSE) confined by the Deng-Fan molecular potential. By employing the Pekeris approximation to resolve the centrifugal singularity and applying the parametric Nikiforov-Uvarov method, we derive closed-form expressions for the energy eigenspectrum and the corresponding radial wavefunctions expressed in terms of Jacobi polynomials. Our investigation reveals that the Dunkl reflection parameter $μ$ fundamentally alters the system's topology by breaking spatial symmetry and introducing a parity-dependent repulsive force. Numerical analysis demonstrates a monotonic increase in energy eigenvalues with increasing $μ$, confirming an effective "hard core" behavior at the origin. The results are shown to be consistent with standard quantum mechanics in the limit $μ\to 0$. This study establishes the Dunkl formalism as a robust tool for modeling quantum systems characterized by parity-dependent exclusion effects and strong short-range correlations. |
| title | Exact Analytical Solutions of the Dunkl-Schrödinger Equation for the Deng-Fan Potential |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.10954 |