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Dirac equation in magnetic-solenoid field

  • S.P. Gavrilov
  • D.M. Gitman
  • A.A. Smirnov
Article

Abstract

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann’s theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.

PACS: 03.65.Pm – 03.65.Ge

Keywords

Boundary Condition Magnetic Field Dirac Equation Uniform Magnetic Field Finite Radius 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag, Società Italiana di Fisica 2003

Authors and Affiliations

  • S.P. Gavrilov
    • 1
  • D.M. Gitman
    • 2
  • A.A. Smirnov
    • 2
  1. 1.Dept. Física e Química, UNESP, Campus de Guaratinguetá, Brazil: On leave from Tomsk State Pedagogical University, 634041Russia
  2. 2.Instituto de Fisica, Universidade de Sao Paulo, CP 66318, CEP 05315-970, Sao Paulo, SPBrasil

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