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

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.

The Equations and Characteristics of the Magnetic Curves in the Sphere Space

“…The magnetic curves on the Riemannian manifolds are trajectories of charged particles moving on under the magnetic field. Meanwhile, the different magnetic fields were extended to different ambient spaces [1][2][3][4][5][6][7][8][9][10][11][12]. Corresponding to parallel Lorentz forces, the magnetic trajectories are obtained on some 2-dimensional space [1,2].…”