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

Vector solutions of the Laplace equation are obtained. Their propertie s and possible applications are discussed. The multipole toroidal mome nts appear naturally in this vector basis, removing the mystery of the ir origin. Conditions are found for the non-radiation of charge and cu rrent densities periodically changing with time. Electromagnetic prope rties of the toroidal solenoid with non-zero helicity, the influence o f the latter on Aharonov-Bohm scattering, and an alternative viewpoint on the toroidal solenoid with non-trivial helicity are studied.