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Exact analytical spectra of an effective field-modified radial Schrödinger equation by the Nikiforov--Uvarov method — arXiv:2610.20159

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.20159
License (as archived): CC0-1.0
Archived: 2026-10-15T14:47:28.516Z
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How to cite

Exact analytical spectra of an effective field-modified radial Schrödinger equation by the Nikiforov--Uvarov method — arXiv:2610.20159 — arXiv (en), https://arxiv.org/abs/2610.20159 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dfa6bed0ef2d (Metraipolis archive dc_dfa6bed0ef2d, sha256 fdb283e425c45f9cbe82867461091ce62c08a6e56d0d051e9c83b47433e52e76)

BibTeX

@misc{dcdfa6bed0ef2d,
  title = {Exact analytical spectra of an effective field-modified radial Schrödinger equation by the Nikiforov--Uvarov method — arXiv:2610.20159},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.20159},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dfa6bed0ef2d; sha256 fdb283e425c45f9cbe82867461091ce62c08a6e56d0d051e9c83b47433e52e76},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.20159. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We revisit the effective radial Schrödinger equation for a charged spinless particle in collinear static electric and magnetic fields that was formulated in our earlier work within the tridiagonal representation approach (TRA). In that model the angular factor of the electric coupling is replaced by the orientation parameter $C=\cos\theta$, the linear Zeeman term is diagonal in the azimuthal quantum number, and the effective field-modified central potential takes the form $V(r)=\Vt(r)+qECr$. Here we show that the same equation can be solved exactly without the TRA, by the Nikiforov--Uvarov (NU) method, once the potential component $\Vt(r)$ is prescribed. Three examples are worked out in closed form: a Kratzer-type component, which yields a linear-plus-Coulomb-plus-inverse-square central potential; a pseudoharmonic-type component, which yields a linear-plus-harmonic-plus-inverse-square potential; and a Hulthén-type component with a repulsive core (Manning--Rosen form), which yields a screened confining potential with a finite number of $s$-wave bound states. For each case we obtain the energy spectrum, the normalized eigenfunctions in terms of Laguerre or Jacobi polynomials, the location of the potential minimum, and closed-form radial moments. The spectra are independent of the orientation $\theta$ and of the electric field, in agreement with the structure found by the TRA, while the field enters through the shape of $V(r)$, the radial moments, and the expectation value $\langle V\rangle_k$. All analytical results are confirmed by an independent finite-difference diagonalization.

Tema degli esploratori: fisica e astronomia (elenco arXiv quant-ph, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.20159 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T14:01:23.660Z dalla pagina https://arxiv.org/list/quant-ph/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).