ABSTRACT
One of the more intriguing and indeed difficult problems in mathematical physics and the applied sciences is the determination of an impurity in an otherwise homogeneous region from the measurements available of an energy field scattered by the inhomogeneity. Such problems frequently arise when analysing various ultrasonic diagnostic techniques and other non-destructive testing processes; typical areas include radar, sonar, geophysics and medical diagnosis. Physical systems such as these can often be modelled in terms of perturbations of the wave equation. When the potential term is independent of time a number of methods are available for tackling the inverse scattering problem. In particular, taking the Fourier transform with respect to time of the plasma wave equation yields a stationary Schrodinger equation. Separation of variable techniques are no longer available and a reduction to the stationary Schrodinger equation is no longer possible. However, a number of authors have studied a plasma wave equation that has a time dependent potential term.
