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Advances in Mathematical Physics
Volume 2016, Article ID 8645732, 8 pages
http://dx.doi.org/10.1155/2016/8645732
Research Article

Description of the Magnetic Field and Divergence of Multisolenoid Aharonov-Bohm Potential

1Azerbaijan State University of Oil and Industry, 1010 Baku, Azerbaijan
2Baku State University, 1148 Baku, Azerbaijan
3Institute of Mathematics and Mechanics of ANAS, 1141 Baku, Azerbaijan
4Jeddah University, Jeddah 21895, Saudi Arabia
5Kafr El-Sheikh University, Kafr El-Sheikh 33516, Egypt

Received 1 September 2015; Accepted 11 January 2016

Academic Editor: Emilio Elizalde

Copyright © 2016 Araz R. Aliev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Explicit formulas for the magnetic field and divergence of multisolenoid Aharonov-Bohm potential are obtained; the mathematical essence of this potential is explained. It is shown that the magnetic field and divergence of this potential are very singular generalized functions concentrated at a finite number of thin solenoids. Deficiency index is found for the minimal operator generated by the Aharonov-Bohm differential expression.