Wave Scattering in 1-d Nonconservative Media
نویسندگان
چکیده
Tuncay Aktosun Department of Mathematics North Dakota State University Fargo, ND 58105 Martin Klaus Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg, VA 24061 Cornelis van der Mee Department of Mathematics University of Cagliari Cagliari, Italy Abstract: In this review paper, the generalized Schr odinger equation d2 =dx2 + k2 = [ikP (x) +Q(x)] is considered, where P (x) and Q(x) are real, integrable potentials with nite rst moments. The scattering solutions and the bound state solutions are studied, the scattering coe cients and their small-k and large-k asymptotics are analyzed. Unless P (x) 0; it is shown that there may be bound states at complex energies, degenerate bound states, and singularities of the transmission coe cient for real k: Some illustrative examples are provided. PACS Numbers: 03.65.Nk, 03.80.+r, 03.40.Kf, 43.20.+g Mathematics Subject Classi cation (1991): 34B24, 34L15, 34L25, 47A40, 81U05
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