A signed particle formulation of nonrelativistic quantum mechanics
Abstract
A formulation of nonrelativistic 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 fieldless 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 timedependent Wigner quasidistribution function of a system and, therefore, the corresponding Schrödinger timedependent wavefunction. 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.
 Publication:

Journal of Computational Physics
 Pub Date:
 September 2015
 DOI:
 10.1016/j.jcp.2015.05.036
 arXiv:
 arXiv:1509.06708
 Bibcode:
 2015JCoPh.297..254S
 Keywords:

 Mathematical formulation of quantum mechanics;
 Newtonian particles;
 Wigner formalism;
 Schrödinger equation;
 Relativistic quantum mechanics;
 Quantum tunnelling;
 Physics  General Physics
 EPrint:
 Journal of Computational Physics, Volume 297, 15 September 2015, Pages 254265