N-dimensional Coulomb-Sturmians with noninteger quantum numbers
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912868212932608 |
|---|---|
| author | Bagci, Ali |
| author_facet | Bagci, Ali |
| contents | Coulomb-Sturmian functions are complete, orthonormal, and include the full spectrum of continuum states. They are restricted to integer values of quantum numbers, as imposed by boundary and orthonormality conditions. Bagci-Hoggan exponential-type orbitals remove this restriction through a generalization to quantum number with fractional order. The differential equations for N-dimensional Bagci-Hoggan orbitals are derived. It is demonstrated that Coulomb-Sturmian functions satisfy a particular case of these equations. Additionally, Guseinov's Psi-alpha-ETOs are identified as N-dimensional Coulomb-Sturmians with a shifted dimensional parameter alpha, rather than representing an independent complete orthonormal sets of basis in a weighted Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01704 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | N-dimensional Coulomb-Sturmians with noninteger quantum numbers Bagci, Ali Quantum Physics Mathematical Physics Coulomb-Sturmian functions are complete, orthonormal, and include the full spectrum of continuum states. They are restricted to integer values of quantum numbers, as imposed by boundary and orthonormality conditions. Bagci-Hoggan exponential-type orbitals remove this restriction through a generalization to quantum number with fractional order. The differential equations for N-dimensional Bagci-Hoggan orbitals are derived. It is demonstrated that Coulomb-Sturmian functions satisfy a particular case of these equations. Additionally, Guseinov's Psi-alpha-ETOs are identified as N-dimensional Coulomb-Sturmians with a shifted dimensional parameter alpha, rather than representing an independent complete orthonormal sets of basis in a weighted Hilbert space. |
| title | N-dimensional Coulomb-Sturmians with noninteger quantum numbers |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2602.01704 |