VECTOR SOLUTIONS OF THE LAPLACE EQUATION AND THE INFLUENCE OF HELICITY ON AHARONOV-BOHM SCATTERING

Vector solutions of the Laplace equation are obtained. Their properties and possible applications are discussed. The multipole toroidal moments appear naturally in this vector basis, removing the mystery of their origin. Conditions are found for the non-radiation of charge and current densities periodically changing with time. Electromagnetic properties of the toroidal solenoid with non-zero helicity, the influence of the latter on Aharonov-Bohm scattering, and an alternative viewpoint on the toroidal solenoid with non-trivial helicity are studied.