THE SEPARABILITY THEOREM REVISITED WITH APPLICATIONS TO LIGHT-SCATTERING THEORY

The separability theorem states that, given a linear partial different ial equation and special coordinates allowing to find a family of sepa rated solutions, all solutions of the equation can be obtained from li near combinations of the separated solutions. In developing a light sc attering theory, it has been recently observed that the theorem may ap parently fail. The separability theorem is therefore revisited and mor e general solutions than usually considered for the scalar wave equati on and the Bromwich scalar potential equation, in cylindrical and sphe rical coordinates, are exhibited. Relevance to light scattering theory is discussed.