Long-range scattering matrix for Schrödinger-type operators

نویسندگان

چکیده

We show that the scattering matrix for a class of Schr\"odinger-type operators with long-range perturbations is Fourier integral operator phase function which generating modified classical map.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Long range scattering for the Wave - Schrödinger system with large wave data and small Schrödinger data

We study the theory of scattering for the Wave-Schrödinger system with Yukawa type coupling in space dimension 3. We prove in particular the existence of modified wave operators for that system with no size restriction on the wave data in the framework of a direct method which requires smallness of the Schrödinger data, and we determine the asymptotic behaviour in time of solutions in the range...

متن کامل

Time-dependent Scattering Theory for Schrödinger Operators on Scattering Manifolds *

We construct a time-dependent scattering theory for Schrödinger operators on a manifold M with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form R×∂M , where ∂M is the boundary of M at infinity. We prove the existence and the completeness of the wave operators, and show that our scattering matrix is equivalent to th...

متن کامل

Quasi exactly solvable matrix Schrödinger operators

Two families of quasi exactly solvable 2 × 2 matrix Schrödinger operators are constructed. The first one is based on a polynomial matrix potential and depends on three parameters. The second is a one-parameter generalisation of the scalar Lamé equation. The relationship between these operators and QES Hamiltonians already considered in the literature is pointed out.

متن کامل

Inverse Scattering for Schrödinger-Type Operators with Interface Conditions Across Smooth Surfaces

We consider direct and inverse scattering for the Laplace-Beltrami operator with electromagnetic potentials in domains with smooth surfaces upon which we impose interface conditions. The boundary conditions used encompass physical models of imperfect transmission arising in acoustics, quantum scattering, semiconductors, and geophysics. We prove uniqueness of the location of the surfaces and the...

متن کامل

Scattering Operators for Matrix Zakharov-Shabat Systems

In this article the scattering matrix pertaining to the defocusing matrix Zakharov-Shabat system on the line is related to the scattering operator arising from time-dependent scattering theory. Further, the scattering data allowing for a unique retrieval of the potential in the defocusing matrix Zakharov-Shabat system are characterized. Mathematics Subject Classification (2000). Primary 34A55, ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Analysis & PDE

سال: 2022

ISSN: ['2157-5045', '1948-206X']

DOI: https://doi.org/10.2140/apde.2022.15.1725