Self-adjoint extensions of the Dirac Hamiltonian in the magnetic-solenoid field and related exact solutions

Journal Article · Sat Feb 01 00:00:00 EST 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.024103· OSTI ID:20633779

Gavrilov, S P; Gitman, D M; Smirnov, A A ^[1]

---

1. Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970 Sao Paulo, Sao Paulo (Brazil)

We study solutions of Dirac equation in the field of Aharonov-Bohm solenoid and a collinear uniform magnetic field. On this base we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We reduce (3+1)-dimensional problem to (2+1)-dimensional one by a proper choice of spin operator. Then we study the problem doing a finite radius regularization of the solenoid field. We exploit solutions of the latter problem to specify boundary conditions in the singular case.

• OSTI ID: 20633779
• Journal Information: Physical Review. A, Vol. 67, Issue 2; Other Information: DOI: 10.1103/PhysRevA.67.024103; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AHARONOV-BOHM EFFECT
BOUNDARY CONDITIONS
DIRAC EQUATION
EXACT SOLUTIONS
HAMILTONIANS
MAGNETIC FIELDS
ONE-DIMENSIONAL CALCULATIONS
QUANTUM ELECTRODYNAMICS
SOLENOIDS
SPIN