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.
Type de document :
Pré-publication, Document de travail
10 pages, 1 figure. 2015
Liste complète des métadonnées

https://hal-enac.archives-ouvertes.fr/hal-01182229
Contributeur : Alexandre Gondran <>
Soumis le : jeudi 30 juillet 2015 - 17:26:46
Dernière modification le : jeudi 11 janvier 2018 - 06:17:30
Document(s) archivé(s) le : mercredi 26 avril 2017 - 08:19:16

Fichiers

particule2D.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • 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. 10 pages, 1 figure. 2015. 〈hal-01182229〉

Partager

Métriques

Consultations de la notice

292

Téléchargements de fichiers

63