https://doi.org/10.1140/epjp/s13360-022-03246-w
Regular Article
Bound states of a relativistic spinning particle in an inhomogeneous magnetic field and its thermodynamic properties
1
Laboratoire LRPPS, Faculté des Sciences et de la Technologie et des Sciences de la Matière, Université Kasdi Merbah Ouargla, 30000, Ouargla, Algeria
2
Département des sciences de la matière, Université de Oum-El-Bouaghi, 04000, Oum El Bouaghi, Algeria
3
Laboratoire de Physique Théorique, Département de Physique, Université de Jijel, BP 98, Ouled Aissa, 18000, Jijel, Algeria
Received:
9
April
2022
Accepted:
30
August
2022
Published online:
16
September
2022
The exact solution of the relativistic spinning particle in the inhomogeneous magnetic field is derived. In this approach, the path integral formalism can analytically eliminate the singularity that we encountered in our study at the point 
, which will give to the kinitic term is a dependent position mass. By using the coordinates transformation, the Green function and the electron propagator are calculated, and the energy eigenvalues and their corresponding eigenfunctions are extracted. The limit case is deduced for a small parameter and the thermodynamic properties are established.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
