Spherically confined hydrogen atom: variational cut-off factor

Authors

  • M. Acosta Roque Universidad Autónoma Metropolitana, Iztapalapa
  • H. Olivares-Pilón Universidad Autónoma Metropolitana, Iztapalapa
  • A. N. Mendoza Tavera Universidad Autónoma Metropolitana, Iztapalapa
  • A. M. Escobar-Ruiz Universidad Autónoma Metropolitana, Iztapalapa

DOI:

https://doi.org/10.31349/SuplRevMexFis.6.011311

Keywords:

confined hydrogen atom, spherical cavity, magnetic field, variational method, cut-off factor, ground state

Abstract

The hydrogen atom confined within an impenetrable spherical cavity of radius R under the influence of a uniform constant magnetic field B is considered. For the ground state, using the variational method, we employ a physically meaningful trial wavefunction characterized by three variational parameters, including a novel cut-off factor that acts as an additional degree of freedom in the optimization process. This approach allows us to systematically analyze the interplay between quantum confinement and the external magnetic field, providing insights into their combined effects on the energy spectrum and wavefunction behavior. Our results reveal how the ground state energy E and eigenfunction evolve as functions of the cavity radius R ∈ [1, 5] a.u. and magnetic field strength B ∈ [0, 1] a.u., offering a deeper understanding of quantum confinement in atomic systems subjected to external fields. These findings have potential implications for confined quantum systems in astrophysical and nanotechnological applications.

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Published

2025-06-12

How to Cite

1.
Acosta Roque M, Olivares-Pilón H, Mendoza Tavera A, Escobar-Ruiz A. Spherically confined hydrogen atom: variational cut-off factor. Supl. Rev. Mex. Fis. [Internet]. 2025 Jun. 12 [cited 2025 Jul. 1];6(1):011311 1-5. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/8003