Wave Scattering in 1-D Nonconservative Media

Tuncay Aktosun, Martin Klaus and Cornelis van der Mee
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Tuncay Aktosun: North Dakota State University, Department of Mathematics
Martin Klaus: Virginia Polytechnic Institute and State University, Department of Mathematics
Cornelis van der Mee: University of Cagliari, Department of Mathematics

Chapter 1 in Spectral and Scattering Theory, 1998, pp 1-18 from Springer

Abstract: Abstract In this review paper, the generalized Schrödinger equation % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWGKbWdamaaCaaaleqabaWdbiaaikdaaaGccqaHipqEcaGGVaGa % amizaiaadIhapaWaaWbaaSqabeaapeGaaGOmaaaakiabgUcaRiaadU % gapaWaaWbaaSqabeaapeGaaGOmaaaakiabeI8a5jabg2da9iaacUfa % caWGPbGaam4AaiaadcfacaGGOaGaamiEaiaacMcacqGHRaWkcaWGrb % GaaiikaiaadIhacaGGPaGaaiyxaiabeI8a5baa!4FE5! $$ {d^2}\psi /d{x^2} + {k^2}\psi = [ikP(x) + Q(x)]\psi $$ is considered, where P(x) and Q(x) are real, integrable potentials with finite first moments. The scattering solutions and the bound state solutions are studied, the scattering coefficients 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 coefficient for real k. Some illustrative examples are provided.

Keywords: Reflection Coefficient; Transmission Coefficient; Exceptional Case; Wave Scattering; SchrOdinger Equation (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-1552-8_1

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DOI: 10.1007/978-1-4899-1552-8_1

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