Self-adjoint Schrodinger and Dirac operators with Aharonov-Bohm and magnetic-solenoid fields

Details Self-adjoint Schrodinger and Dirac operators with Aharonov-Bohm and magnetic-solenoid fields Self-adjoint Schrodinger and Dirac operators with Aharonov-Bohm and magnetic-solenoid fields

2009-11-04

arxiv.org/abs/0911.0946v1

Physics

Quantum Physics

38 pages

Scientific paper

We study all the s.a. Schrodinger and Dirac operators (Hamiltonians) both with pure AB field and with magnetic-solenoid field. Then, we perform a complete spectral analysis for these operators, which includes finding spectra and spectral decompositions, or inversion formulas. In constructing the Hamiltonians and performing their spectral analysis, we respectively follow the von Neumann theory of s.a. extensions of symmetric differential operators and the Krein method of guiding functionals. The examples of similar consideration are given by us in arXiv:0903.5277, where a nonrelativistic particle in the Calogero potential field is considered and in Theor. Math. Phys. 150 (1) (2007) 34, where a Dirac particle in the Coulomb field of arbitrary charge is considered. However, due to peculiarities of the three-dimensional problems under consideration, we elaborated a generalization of the approach used in the study of the Dirac particle.

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