Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# Bohmian Quantum Mechanics Revisited

Version 1 : Received: 14 August 2018 / Approved: 15 August 2018 / Online: 15 August 2018 (03:44:18 CEST)
Version 2 : Received: 30 August 2018 / Approved: 31 August 2018 / Online: 31 August 2018 (05:39:53 CEST)

How to cite: Arbab, A. Bohmian Quantum Mechanics Revisited. Preprints 2018, 2018080260 (doi: 10.20944/preprints201808.0260.v2). Arbab, A. Bohmian Quantum Mechanics Revisited. Preprints 2018, 2018080260 (doi: 10.20944/preprints201808.0260.v2).

## Abstract

By expressing the Schrödinger wave function in the form $\psi =R{e}^{iS/\hslash }$ , where R and S are real functions, we have shown that the expectation value of S is conserved. The amplitude of the wave (R) is found to satisfy the Schrödinger equation while the phase (S) is related to the energy conservation. Besides the quantum potential that depends on R, viz., ${V}_{Q}=-\frac{{\hslash }^{2}}{2m}\frac{{\nabla }^{2}R}{R}$ , we have obtained a spin potential ${V}_{S}=-\frac{S{\nabla }^{2}S}{m}$ that depends on S which is attributed to the particle spin. The spin force is found to give rise to dissipative viscous force. The quantum potential may be attributed to the interaction between the two subfields S and R comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass $m{c}^{2}$ with an internal frequency of $2m{c}^{2}/\hslash$ , 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 R satisfies the Klein-Gordon equation, then S must satisfies the wave equation. Conversely, if R satisfies the wave equation, then S yields the Einstein relativistic energy momentum equation.

## Subject Areas

quantum mechanics; bohmian quantum mechanics; quantum potential; schrodinger equation; dirac equation; klein-gordon equation; spin

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