Abstract
In order to clarify physical consequences due to the presence of a set of auxiliary functionsφ k (q,t) in quantum mechanics with a non-negative phase-space distribution function, the simplest quantum-mechanical problems are solved. It is shown thatφ k (q,t) influence upon the results of a problem. Therefore it is supposed thatφ k (q, t) reflect some physical reality (subquantum situation), interacting with a mechanical system. In particular the ‘subquantum situation’ determines the minimum coordinate and momentum uncertainties ((δq)2 and (δp)2) as well as the coordinate distribution of a ‘fixed’ system and the momentum distribution of a ‘free’ system. These results provide the opportunity to formulate the notion of a stationary homogeneous isotropic ‘subquantum situation’. Supposing thatδq andδp are small an attempt is made to develop an approximate method of solutions (quasi-orthodox approximation). Energy spectrum of an electron in a hydrogen atom is found in the second order of this approximation.
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On leave of absence from Peoples' Friendship University, Chair of Theoretical Physics, 3, Ordjonikidze Street, B-302, Moscow, U.S.S.R.
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Kuryshkin, V.V. Some problems of quantum mechanics possessing a non-negative phase-space distribution function. Int J Theor Phys 7, 451–466 (1973). https://doi.org/10.1007/BF00713247
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DOI: https://doi.org/10.1007/BF00713247