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Eigenfunction expansions associated with the Schrödinger operator with a complex potential and the scattering theory. (English) Zbl 0197.53501
The main purpose of the paper is to give a generalization of the eigenfunction expansion and scattering theory developed by A. Ya. Povzner [Mat. Sb., N. Ser. 32(74), 109–156 (1953; Zbl 0050.32201], L. D. Faddeev [Uniqueness of solution of the inverse scattering problem. (Russian). Vestn. Leningr. Univ. 11, No. 7, Ser. Mat. Mekh. Astron. No. 2, 126–130 (1956)] and T. Ikebe [Arch. Ration. Mech. Anal. 5, 1–34 (1960; Zbl 0145.36902)] for the selfadjoint Schrödinger operator in \(E_3\) to the non-selfadjoint case. The results are obtained in general under a typical limiting condition on the potential. The last sections contain a discussion of the time-dependent scattering theory and of the uniqueness of the solution for the scattering inverse problem.
Reviewer: P. Gulmanelli

MSC:
35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators
Keywords:
quantum theory
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