2015/10/22 by Maaneli Derakhshani, Derakhshani, Maaneli
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1510.06391
openalex publication_date 2015/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Wallstrom's criticism of existing formulations of stochastic mechanics is that they fail to derive the empirical predictions of orthodox quantum mechanics because they require an ad hoc quantization condition on the postulated velocity potential, S, in order to derive Schrödinger wave functions. We propose an answer to this criticism by modifying the Nelson-Yasue formulation of non-relativistic stochastic mechanics for a spinless particle with the following hypothesis: a spinless Nelson-Yasue particle of rest mass m continuously undergoes a driven steady-state oscillation of `zitterbewegung' (zbw) frequency, ωc=(1/ℏ)mc2, in its instantaneous mean forward (and backward) translational rest frame. With this hypothesis we show that, in the lab frame, S arises from imposing the constraint of conservative diffusions on the time-symmetrized steady-state phase of the zbw particle, satisfies the required quantization condition, and evolves in time by the Hamilton-Jacobi-Madelung equations (when generalized to describe a statistical ensemble of zbw particles). From the mathematical equivalence of Schrödinger's equation with the Hamilton-Jacobi-Madelung equations plus the quantization condition, Schrödinger wave functions for a spinless particle (in and excluding external fields) are thereby recovered. We also apply this `zitterbewegung stochastic mechanics' (ZSM) to the case of a central potential and show that it predicts angular momentum quantization. This paper sets the foundation for Part II, which will (primarily) work out the many-particle version of ZSM.