A signed particle formulation of non-relativistic quantum mechanics
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 Schrödinger 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.
- 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
- E-Print:
- Journal of Computational Physics, Volume 297, 15 September 2015, Pages 254-265