1. For a survey of this inverse problem, see Faddeyev, L. D.: The inverse problem in the quantum theory of scattering. J. Math. Phys.4, 72 (1963).
2. Newton, R. G.: Scattering theory of waves and particles, Chapter 20. New York: Mc Graw-Hill Book Company, 1966.
3. Gel'fand, I. M., Levitan, B. M.: On the determination of a differential equation from its spectral function. Izvest. Akad. Nauk S.S.S.R.15, 309 (1951); translated in Am. Math. Soc. Transl.1, 253 (1955).
4. For the Marchenko method, see the book of Agranovich, Z. S., Marchenko, V. A.: The inverse problem of scattering theory. New York: Gordon and Breach 1963.
5. In the case of a complex energy-independent potential, this assumption has already been used by Gasymov, M. G.: Doklad. Akad. Nauk S.S.S.R.165, 261 (1965), see also Bertero, M., Dillon, G.: An outline of scattering theory for absorptive potentials. Nuovo Cimento2 A, 1024 (1971).