The quantum mechanics of high-order kinematic values

In this paper, within the framework of a unified mathematical model, the new formulation of quantum mechanics – quantum mechanics of higher order kinematic values – is proposed. In contrast to the well-known formulations of quantum mechanics in the new formulation, the wave function has not only a c...

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Bibliographic Details
Published in:Annals of physics 2019-02, Vol.401, p.59-90
Main Authors: Perepelkin, E.E., Sadovnikov, B.I., Inozemtseva, N.G.
Format: Article
Language:English
Subjects:
ALGEBRA
BOLTZMANN-VLASOV EQUATION
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
ENTROPY
High order mechanics
MATHEMATICAL MODELS
PSI-algebra
QUANTUM MECHANICS
QUANTUM SYSTEMS
Rigorous result
Vlasov equation
WAVE FUNCTIONS
Wigner function
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Summary:In this paper, within the framework of a unified mathematical model, the new formulation of quantum mechanics – quantum mechanics of higher order kinematic values – is proposed. In contrast to the well-known formulations of quantum mechanics in the new formulation, the wave function has not only a coordinate or momentum representation, but also representations through acceleration and accelerations of higher orders. The representations of the wave function in terms of higher order kinematic values make it possible to consider the dissipative systems problem and the variable entropy systems one within a single mathematical apparatus. The new formulation is not built phenomenologically, but from first principles and in a particular case contains the formulation of the de Broglie–Bohm 〈wave-pilot〉 quantum mechanics. The new formulation is based on the Vlasov equations chain. This approach allows us to obtain a natural connection between classical and quantum systems. Examples of such systems are considered in this paper.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2018.12.001