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

S. Alvarez, R. Acosta, R. de Coss

Abstract


The quantization method applied to the hydrogen atom involves the solution of the phase integral $\oint p_r\,dr=n_r h$, which was named by Sommerfeld as the \textit{radial quantum condition} and solved using complex integration. In this work, we present an alternative solution to the \textit{radial quantum condition} using standard integration methods as an accessible way for students of introductory quantum mechanics courses. In addtion, 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.


Keywords


Hydrogen atom, elliptical orbits, phase integral.

Full Text:

PDF


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

Refbacks

  • There are currently no refbacks.


Revista Mexicana de Física E

ISSN: 2683-2216 (on line), 1870-3542 (print)

Semiannual publication of Sociedad Mexicana de Física, A.C.
Departamento de Física, 2o. Piso, Facultad de Ciencias, UNAM.
Circuito Exterior s/n, Ciudad Universitaria. C. P. 04510 Ciudad de México.
Apartado Postal 70-348, Coyoacán, 04511 Ciudad de México.
Tel/Fax: (52) 55-5622-4946, (52) 55-5622-4840. rmf@ciencias.unam.mx