EIGENFUNCTIONS OF THE CURL OPERATOR IN SPHERICAL COORDINATES

The eigenfunctions of the curl operator are obtained by separation of variables in spherical coordinates, making use of the spin-weighted spherical harmonics. It is shown that the eigenfunctions of the curl operator with vanishing divergence can be written in terms of a single scalar potential that satisfies the Helmholtz equation. It is also shown that these eigenfunctions give a complete basis for the divergenceless vector fields.