Journal of East China Normal University(Natural Science) >

2022 , Vol. 2022 >Issue 4: 95 - 102

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.04.009

Physics and Electronics

Foldy-Wouthuysen transformation of the (2 + 1)-dimensional Dirac oscillator

  • Wei SUN ,
  • Keye ZHANG
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  • School of Physics and Electronic Science, East China Normal University, Shanghai　200241, China

Received date: 2021-04-16

  Online published: 2022-07-19

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Abstract

The (2 + 1)-dimensional Dirac oscillator is a fundamental model used to study the relativistic extensions of quantum effects and principles. Due to the influence of relativistic effects, including the non-equidistant and negative excitation spectrum and the spin-orbit coupling, the eigenstates are complicated dressed states composed of spin and angular momentum state vectors; in turn, this renders theoretical research difficult. In this work, we decouple the spin and angular momentum state vectors and separate the spin-up and -down components into positive- and negative-energy states, respectively, using the Foldy-Wouthuysen (F-W) transformation. The Hamiltonian and eigenstates of the Dirac oscillator are then largely simplified in the F-W representation; nevertheless, we find the forms of the operators for spin and angular momentum in the same representation with complex combinations of each other. The results are useful in advancing research in relativistic quantum mechanics and spin-orbit coupling.

Key words： Dirac oscillator; dressed states; Foldy-Wouthuysen transformation

Cite this article

Wei SUN , Keye ZHANG . Foldy-Wouthuysen transformation of the (2 + 1)-dimensional Dirac oscillator[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(4) : 95 -102 . DOI: 10.3969/j.issn.1000-5641.2022.04.009

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