2012/04/06 by Maxim Raykin, Raykin, Maxim
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1204.1540
64 pages, LaTeX; v2: minor stylistic corrections; v3: modified conclusion section, several minor changes in other sections; v4: introduction, conclusion, and part of section 3 rewritten, two figures added, several other minor changes
arxiv created 2012/07/11 · arxiv updated 2012/07/12
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics to the quantum domain, and turns into them in the classical limit ℏ→ 0. The particles' motions are completely determined by the initial conditions. In this theory, the wave function ψ of quantum mechanics is equal to the exponent of an action function, obtained by integrating some Lagrangian function along particle trajectories, described by equations of motion. Consequently, the equation for the logarithm of a wave function is related to the equations of motion in the same way as the Hamilton-Jacobi equation is related to the Hamilton equations in classical mechanics. We demonstrate that the probability density of particles, moving according to these equations, should be given by a standard quantum-mechanical relation, ρ=|ψ|2. The theory of quantum measurements is presented, and the mechanism of nonlocal correlations between results of distant measurements with entangled particles is revealed. In the last section, we extend the theory to particles with nonzero spin.