Quantization in classical mechanics and its relation to the Bohmian {Psi}-field

Journal Article · Mon Aug 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.04.012· OSTI ID:21583325

Vlasenko, D S ^[1]; Mavrodiev, S Cht ^[2]

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1. Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, 65044 Odessa (Ukraine)
2. The Institute for Nuclear Research and Nuclear Energy, BAS, 1874 Sofia (Bulgaria)

Research highlights: > The Schroedinger equation is derived from the classical Hamiltonian mechanics. > This derivation is based on the Chetaev theorem on stable dynamical trajectories. > The conditions for correctness of trajectory quantum mechanics are discussed. - Abstract: Based on the Chetaev theorem on stable dynamical trajectories in the presence of dissipative forces, we obtain the generalized condition for stability of Hamilton systems in the form of the Schroedinger equation. It is shown that the energy of dissipative forces, which generate the Chetaev generalized condition of stability, coincides exactly with the Bohm 'quantum' potential. Within the frame-work of Bohmian quantum mechanics supplemented by the generalized Chetaev theorem and on the basis of the principle of least action for dissipative forces, we show that the squared amplitude of a wave function in the Schroedinger equation is equivalent semantically and syntactically to the probability density function for the number of particle trajectories, relative to which the velocity and the position of the particle are not hidden parameters. The conditions for the correctness of trajectory interpretation of quantum mechanics are discussed.

• OSTI ID: 21583325
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 8; Other Information: DOI: 10.1016/j.aop.2011.04.012; PII: S0003-4916(11)00071-6; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
HAMILTONIANS
POTENTIALS
PROBABILITY DENSITY FUNCTIONS
QUANTIZATION
QUANTUM MECHANICS
SCHROEDINGER EQUATION
STABILITY
TRAJECTORIES
VELOCITY
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
WAVE EQUATIONS