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Remark on the three-dimensional mixed impedance potential equation

The mixed impedance potential equation is ( alpha -2 Del . alpha 2 Del +k2-V) phi (k,x)=0 where V(x) is a 'good potential' (i.e. it ensures scattering theory) and alpha is such that alpha -1 Delta alpha is also a 'good potential' everywhere in R3 except on a finite number of surfaces across which alpha and Del alpha show jumps. Adequate continuity conditions are imposed on phi and Del phi , and many equations of mathematical physics can be reduced to special cases of this equation. The author shows how a standard transformation can put 'continuous parts' of alpha into V and vice versa without modifying the scattering problem. Hence there is a standard ambiguity in any inverse problem connected with this equation.