Elliptical orbits in the phase-space quantization
Quantum Physics
2016-07-15 v2
Abstract
The energy levels of hydrogen-like atoms are obtained from the phase-space quantization, one of the pillars of the old quantum theory, by three different methods - (i) direct integration, (ii) Sommerfeld's original method, and (iii) complex integration. The difficulties come from the imposition of elliptical orbits to the electron, resulting in a variable radial component of the linear momentum. Details of the calculation, which constitute a recurrent gap in textbooks that deal with phase-space quantization, are shown in depth in an accessible fashion for students of introductory quantum mechanics courses.
Cite
@article{arxiv.1605.08027,
title = {Elliptical orbits in the phase-space quantization},
author = {Leonardo Andreta de Castro and Carlos Alexandre Brasil and Reginaldo de Jesus Napolitano},
journal= {arXiv preprint arXiv:1605.08027},
year = {2016}
}