Generation of solutions of linear differential equations
In [1] Moseley derived some nonseparable solutions of the Helmholtz equation, and in [2] he demonstrated how these solutions could be generated by applying a certain differential operator to a separable solution. In the present paper we point out that Moseley's method applies in greater generality to any linear partial differential equation, and, indeed, to any linear operator equation. Suppose L is a linear operator and that w is any solution to the equation