Further properties of the nonseparable solutions of the Helmholtz wave equation

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Abstract
Nonseparable solutions W ( n ) {W^{\left ( n \right )}} of ( ∇ 2 + k 2 ) W ( n ) = 0 \left ( {{\nabla ^2} + {k^2}} \right ){W^{\left ( n \right )}} = 0 are linearly independent, but inter-related through a generative differential operator. The nonseparable of order n = 0 n = 0 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.

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