Elliptical orbits in the phase-space quantization

• Autor(a) principal: Castro,Leonardo Andreta de
• Data de Publicação: 2016
• Outros Autores: Brasil,Carlos Alexandre, Napolitano,Reginaldo de Jesus
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Revista Brasileira de Ensino de Física (Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172016000300418
• topic: old quantum mechanics; phase-space quantization

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.