A Signed Particle Formulation of Non-Relativistic Quantum Mechanics

TL;DR

This paper introduces a new signed particle formulation of non-relativistic quantum mechanics, describing quantum systems as ensembles of classical-like particles with signs, capable of reproducing quantum phenomena and extending to relativistic effects.

Contribution

It presents a set of three postulates for a particle-based quantum formulation, generalizes the signed particle Wigner Monte Carlo method, and discusses extensions to relativistic regimes.

Findings

Successfully reproduces quantum tunneling phenomena

Provides a classical-like interpretation of quantum mechanics

Extends the signed particle approach to relativistic effects

Abstract

A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schroedinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.