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Posted: May 26, 2015

A new formulation of quantum mechanics

(Nanowerk News) Quantum mechanics remains one of the most tested theory in the history of physics and yet it represents one of the most challenging theory human kind has come up with. While the Schrödinger formulation is the de-facto standard, describing systems in terms of wave-functions, it is certainly not the only approach possible. Other formalisms are possible too.
For example the path integral method, suggested by R. Feynman, is one possibility to describe systems in terms of classical particles.
Another method is the one suggested by E. Wigner where systems are described in terms of (quasi-)distribution functions, therefore allowing quantum mechanics in the phase-space.
Recently, a new formulation of quantum mechanics has been developed, called the "Signed particle formulation". This novel theory has been suggested by Dr. J.M. Sellier, an Associate Professor at the Bulgarian Academy of Sciences.
This new approach to quantum systems is based on classical particles which interact with external potentials by means of creation and annihilation of signed particles only. This novel theory is based on rewriting the time-dependent Wigner equation and on giving a physical interpretation to the various mathematical terms obtained.
In particular the sign of a particle, perhaps the most puzzling new introduced feature, has a physical interpretation based on observations in the context of quantum tomography.
This new theory provides several advantages:
  • Simple picture of the quantum world: Quantum systems are described by ensembles of classical particles which provides a whole range of statistical information close to the language of experimentalists.
  • Simplicity of implementation: The description of systems is based on evolving particles which are trivial to implement in a computer program. Moreover a working implementation in C is available
  • Parallelization: Signed particles are independent from each other, therefore providing a way for incredible levels of parallelization.
  • Classical limit: The transition from quantum to classical systems becomes practically trivial in this new formulation.
  • A preprint of the paper, which was accepted a few days ago on the Journal of Computational Physics is available online: "A Signed Particle Formulation of Non-Relativistic Quantum Mechanics" (pdf).
    Source: Bulgarian Academy of Sciences
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