Abstract
In preceding studies by the present author, it has been shown that in quantum mechanics formulated in the framework of theK-field formalism, Lyapunov-stable solutions of the equations ofK-motions describing the dynamics of a test point particle which models the behavior of a microscopic particle from the standpoint of classical mechanics may be selected as the quantization criterion. The present article is concerned with methods of obtaining a stability condition in explicit form.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. B. Korotchenko, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 12, 55–58 (1983); No. 8, 119–121 (1984); No. 3, 30–32 (1987); No. 10, 76–80 (1990).
K. B. Korotchenko, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 12, 30–33 (1995).
B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).
M. M. Khapaev, Averaging in Stability Theory. The Investigation of Multiparticle Resonance Systems [in Russian], Nauka, Moscow (1986).
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space [in Russian], Nauka, Moscow (1970).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 42–45, January, 1996.
Rights and permissions
About this article
Cite this article
Korotchenko, K.B. Stability of the solution of a special type of self-consistent problem. Russ Phys J 39, 37–40 (1996). https://doi.org/10.1007/BF02069238
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02069238