Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field

Details Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field

2001-11-08

arxiv.org/abs/quant-ph/0111050v1

J. Math. Phys. 43 (2002), 2151-2168

Physics

Quantum Physics

32 pages, a LaTeX source file with 2 eps figures; submitted to J. Math. Phys

Scientific paper

10.1063/1.1463712

The most general admissible boundary conditions are derived for an idealised Aharonov-Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; other two parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic field. The generalised boundary conditions may be regarded as a combination of the Aharonov-Bohm effect with a point interaction. Spectral properties of the derived Hamiltonians are studied in detail.

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