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Bohmian quantum mechanics revisited

Quantum Physics 2018-10-09 v2

Abstract

By expressing the Schr\"odinger wave function in the form ψ=ReiS/\psi=Re^{iS/\hbar}, where RR and SS are real functions, we have shown that the expectation value of SS is conserved. The amplitude of the wave (RR) is found to satisfy the Schr\"odinger equation while the phase (SS) is related to the energy conservation. Besides the quantum potential that depends on RR, \emph{viz.}, VQ=22m2RRV_Q=-\frac{\hbar^2}{2m}\frac{\nabla^2R}{R}\,, we have obtained a phase potential VS=S2SmV_S=-\frac{S\nabla^2S}{m} that depends on the phase SS derivative. The phase force is a dissipative force. The quantum potential may be attributed to the interaction between the two subfields SS and RR comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass mc2mc^2 with an internal frequency of 2mc2/2mc^2/\hbar, satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz RR satisfies the Klein-Gordon equation, then SS must satisfies the wave equation. Conversely, if RR satisfies the wave equation, then SS yields the Einstein relativistic energy momentum equation.

Keywords

Cite

@article{arxiv.1710.01256,
  title  = {Bohmian quantum mechanics revisited},
  author = {A. I. Arbab},
  journal= {arXiv preprint arXiv:1710.01256},
  year   = {2018}
}

Comments

11 LaTeX pages, no figures

R2 v1 2026-06-22T22:02:38.929Z