Relation between the Schrödinger equation and the plasma wave equation

Scattering theories for the time-independent Schrödinger equation and for the plasma wave equation in $R^3$ are compared. If V-Δ has no point eigenvalues, the relevant quantities in both theories are simply related by Fourier transformation, but if V-Δ has eigenvalues, then retarded pulse solutions of the plasma wave equation are shown to grow exponentially with time and no physically meaningful scattering theory appears possible for that equation.