An alternative solution to the radial quantum condition for the hydrogen atom

Authors

  • S. Alvarez Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados del IPN http://orcid.org/0000-0003-2478-8739
  • R. Acosta Facultad de Ciencias Quimicas, Universidad Central de Ecuador, Quito, Ecuador.
  • R. de Coss Departamento de Fisica Aplicada, Centro de Investigacion y de Estudios Avanzados del IPN, A.P. 73 Cordemex 97310 Merida, Yucatan, Mexico.

DOI:

https://doi.org/10.31349/RevMexFisE.17.1

Keywords:

Hydrogen atom, elliptical orbits, phase integral.

Abstract

The quantization method applied to the hydrogen atom involves the solution of the phase integral H pr dr = nrh, which was named by Sommerfeld as the radial quantum condition and it was solved using complex integration. In this work, we present an alternative solution to the radial quantum condition using real variable integration methods as an accessible way for students of introductory quantum mechanics courses. In addition, we show that in the Sommerfeld model the degeneracy of the energy levels is related to the geometric properties of the ellipse describing the electron motion around the nucleus.

Author Biography

S. Alvarez, Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados del IPN

Investigador Cinvestav 3C

Departamento de Física Aplicada

Cinvestav-Mérida

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Published

2020-01-28

How to Cite

[1]
S. Alvarez, R. Acosta, and R. de Coss, “An alternative solution to the radial quantum condition for the hydrogen atom”, Rev. Mex. Fis. E, vol. 17, no. 1 Jan-Jun, pp. 1–5, Jan. 2020.

Issue

Vol. 17 No. 1 Jan-Jun (2020): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2020 Romeo de Coss

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.