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On the Linear Forms of the Schrödinger Equation

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Abstract

Generalising the linearisation procedure used by Dirac and later by Lévy-Leblond, we derive the first-order non-relativistic wave equations for particles of spin 1 and spin 3/2 starting from the Schrödinger equation. By the introduction in the momentum of a correction linear in coordinates, we establish the wave equation of the radial harmonic oscillator with spin-orbit coupling.

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Acknowledgements

We would like to thank Hervé Mohrbach for very stimulating discussions.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Université Abderrahmane Mira de Béjaia, Campus de Targa Ouzemour, Dz-06000, Béjaia, Algeria

    Y. Kasri

  2. Institut de Physique, Equipe BioPhyStat, ICPMB, IF CNRS 2843, Université Paul Verlaine-Metz, 1 Bd. Arago, 57078, Metz, Cedex 3, France

    Y. Kasri, A. Bérard & Y. Grandati

  3. Département de Physique, Faculté des Sciences Exactes, Université Mentouri Constantine, Constantine, Algérie

    L. Chetouani

Authors
  1. Y. Kasri
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  2. A. Bérard
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  3. Y. Grandati
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  4. L. Chetouani
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Correspondence to A. Bérard.

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Kasri, Y., Bérard, A., Grandati, Y. et al. On the Linear Forms of the Schrödinger Equation. Int J Theor Phys 51, 1370–1378 (2012). https://doi.org/10.1007/s10773-011-1012-7

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  • DOI: https://doi.org/10.1007/s10773-011-1012-7

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