SMALL-ENERGY ASYMPTOTICS FOR THE SCHRÖDINGER EQUATION ON THE LINE Dedicated to Pierre C. Sabatier on the occasion of his 65th birthday
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چکیده
The one-dimensional Schrödinger equation is considered when the potential is real valued, integrable, and has a finite first moment. The small-energy asymptotics of the logarithmic spatial derivative of the Jost solutions are established. Some consequences of these asymptotics are presented such as the small-energy limits of the scattering coefficients and a simplified characterization of the scattering data for the inverse scattering problem. When the potential also has a finite second moment, some improved results are given on the small-energy asymptotics of the scattering coefficients and the logarithmic spatial derivatives of the Jost solutions. PACS Numbers (1999): 02.60.Lj, 03.65.Nk Mathematics Subject Classification (2000): 34L25, 34L40, 81U05, 81U40
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تاریخ انتشار 2007