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arXiv · 1605.08027

Elliptical orbits in the phase-space quantization

Leonardo Andreta de Castro·Carlos Alexandre Brasil·Reginaldo de Jesus Napolitano
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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.

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Leonardo Andreta de Castro, Carlos Alexandre Brasil, Reginaldo de Jesus Napolitano. 2016-07-14. Elliptical orbits in the phase-space quantization. https://doi.org/10.1590/1806-9126-rbef-2016-0067

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