Classical stochastic representation of quantum mechanics
Statistical Mechanics
2023-08-02 v1 Quantum Physics
Abstract
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension into a Hilbert space of dimension which is obtained by a peculiar canonical transformation that changes a pair of real canonical variables into a pair of complex canonical variables which are complex conjugate of each other. The probabilistic character of quantum mechanics is devised by treating the wave function as a stochastic variable. The dynamics of the underlying system is chosen so as to preserve the norm of the state vector.
Cite
@article{arxiv.2308.00151,
title = {Classical stochastic representation of quantum mechanics},
author = {Mário j. de Oliveira},
journal= {arXiv preprint arXiv:2308.00151},
year = {2023}
}