Eur. Phys. J. C 32, s1.119-s1.142 (2004)
DOI: 10.1140/epjcd/s2003-01-009-1

Dirac equation in magnetic-solenoid field

S.P. Gavrilov¹, D.M. Gitman² and A.A. Smirnov<sup>2

1</sup>  Dept. Física e Química, UNESP, Campus de Guaratinguetá, Brazil: On leave from Tomsk State Pedagogical University, 634041, Russia
²  Instituto de Fisica, Universidade de Sao Paulo, CP 66318, CEP 05315-970, Sao Paulo, SP, Brasil

gavrilovsp@hotmail.com
gitman@dfn.if.usp.br
saa@dfn.if.usp.br

(Received 21 March 2003 / Published online 10 June 2003)

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

© Società Italiana di Fisica, Springer-Verlag 2004