A heuristic extended particle 2D-model compatible with quantum mechanics

Abstract : In this paper we propose an extended particle model whose evolution is deterministic. In dimension 2, the extended particle is represented by four points that define a small elastic string that vibrates, alternating between a creation process and an annihilation process. First we show how the spin and the Heisenberg uncertainty relations emerge from this extended particle. We then show how the complex action associated with this extended particle satisfies, from a generalized principle of least action, a second order complex Hamilton-Jacobi equation. Third, we show that the wave function, which admits this action as a complex phase, satisfies the Schrödinger equation. Finally, we show that the gravity center of this extended particle follows the trajectories proposed by the de Broglie-Bohm interpretation well as the Schrödinger interpretation. This model is built on two new mathematical concepts we have introduced: complex analytical mechanics on complex-valued functions and a periodic deterministic process.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal-enac.archives-ouvertes.fr/hal-01182229
Contributor : Alexandre Gondran <>
Submitted on : Thursday, July 30, 2015 - 5:26:46 PM
Last modification on : Wednesday, July 24, 2019 - 11:48:01 PM
Long-term archiving on: Wednesday, April 26, 2017 - 8:19:16 AM

Files

particule2D.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01182229, version 1
  • ARXIV : 1507.08777

Collections

Citation

Michel Gondran, Alexandre Gondran. A heuristic extended particle 2D-model compatible with quantum mechanics. 2015. ⟨hal-01182229⟩

Share

Metrics

Record views

317

Files downloads

88