Resonances for steplike potentials: Forward and inverse results
نویسندگان
چکیده
منابع مشابه
Resonances for Steplike Potentials: Forward and Inverse Results
We consider resonances associated to the one dimensional Schrödinger operator − d 2 dx2 + V (x), where V (x) = V+ if x > xM and V (x) = V− if x < −xM , with V+ = V−. We obtain asymptotics of the resonance-counting function for several regions. Moreover, we show that in several situations, the resonances, V+, and V− determine V uniquely up to translation.
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در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Reconstruction of Steplike Potentials
In this article we study some numerical methods for the determination of a potential V (x) in the one dimensional Schrödinger equation. We assume that V (x) = 0 for x < 0, and tends to a nonnegative constant as x tends to positive infinity. We suppose also that there are no bound states. The approach pursued here is a based on a transformation to an equivalent ‘time domain’ problem, namely the ...
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We develop direct and inverse scattering theory for one-dimensional Schrödinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.
متن کاملInverse Scattering Theory for One-dimensional Schrödinger Operators with Steplike Finite-gap Potentials
We develop direct and inverse scattering theory for one-dimensional Schrödinger operators with steplike potentials which are asymptotically close to different finite-gap potentials on different half-axes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03716-5