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Hydrogen atom in quantum mechanics and quantization on curved surfaces

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Abstract

New quantization rules for classical systems are obtained using the Titchmarsh expansion. These rules generalize the conventional ones and are reduced to them when a transition to Cartesian coordinates exists. An equation generalizing the Schrödinger equation to arbitrary natural systems is found. The principle of minimal constraint (strong equivalence principle) makes it possible to extend this equation to any curved spaces.

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Authors and Affiliations

  1. St. Petersburg State Technical University, ul. Politekhnicheskaya 29, St. Petersburg, 195251, Russia

    A. G. Chirkov & A. Ya. Berdnikov

Authors
  1. A. G. Chirkov
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  2. A. Ya. Berdnikov
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__________

Translated from Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 71, No. 4, 2001, pp. 6–12.

Original Russian Text Copyright © 2001 by Chirkov, Berdnikov.

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Chirkov, A.G., Berdnikov, A.Y. Hydrogen atom in quantum mechanics and quantization on curved surfaces. Tech. Phys. 46, 368–374 (2001). https://doi.org/10.1134/1.1365457

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