A Signed Particle Formulation of Non-Relativistic Quantum Mechanics

By Jean Michel D Sellier

Bulgarian Academy of Sciences

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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 Schr¨odinger 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.

http://www.sciencedirect.com/science/article/pii/S0021999115003708

 

References

J.M. Sellier, "A Signed Particle Formulation of Non-Relativistic Quantum Mechanics", Journal of Computational Physics, Volume 297, Pages 254–265, DOI: 10.1016/j.jcp.2015.05.036, (2015).

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Researchers should cite this work as follows:

  • Jean Michel D Sellier (2015), "A Signed Particle Formulation of Non-Relativistic Quantum Mechanics," http://nanohub.org/resources/22390.

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Tags

  1. formulation of quantum mechanics
  2. Newtonian particles
  3. Wigner
  4. Schroedinger
  5. Relativity
  6. tunnelling