Further properties of the nonseparable solutions of the Helmholtz wave equation
Abstract: Nonseparable solutions of are linearly independent, but inter-related through a generative differential operator. The nonseparable of order is the familiar separable solution. In two cartesian coordinates, a sum of zero and second order solutions can describe transverse motion of a membrane of unique boundary contour. In three coordinates the same sum can describe acoustic pressure in a uniquely shaped cavity with pressure-release walls.
-  Donald S. Moseley, Non-separable solutions of the Helmholtz wave equation, Quart. Appl. Math. 22 (1965), 354–357. MR 0183970, https://doi.org/10.1090/S0033-569X-1965-0183970-3
-  Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774