Titlebook: Direct and Inverse Scattering for the Matrix Schrödinger Equation; Tuncay Aktosun,Ricardo Weder Book 2021 Springer Nature Switzerland AG 2

Thyroxine

https://doi.org/10.1007/978-3-662-58125-4ith the general self-adjoint boundary condition. We show how the analysis of star graphs and the Schrödinger scattering problem on the full line can be reduced to the study of the matrix Schrödinger equation on the half line with some appropriate self-adjoint boundary conditions. To analyze the dire

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ingenue

https://doi.org/10.1007/978-3-662-58125-4of the wave operators introduced by Møller. The role of the limiting absorption principle is indicated, and it is shown how the Hamiltonian and its resolvent are related to the potential and the two boundary matrices describing the general self-adjoint boundary condition. The generalized Fourier map

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https://doi.org/10.1007/978-3-662-58125-4a set . in the Marchenko class. We discuss the nonuniqueness arising in the inverse scattering problem if the scattering matrix is defined one way with the Dirichlet boundary condition and in a different way with a non-Dirichlet boundary condition, as usually done in the standard literature. We pres

Ostrich

https://doi.org/10.1007/978-3-662-58125-4xplicitly solved examples when its kernel contains a matrix exponential and hence becomes separable. The necessity of the integrability of the potential is demonstrated when a general self-adjoint boundary condition is used rather than only the Dirichlet boundary condition. The characterization of t

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Offbeat

Direct Scattering I,tion of the boundary condition are explicitly constructed from the scattering data set. We analyze the bound states and prove Levinson’s theorem, showing how a change in the phase of the determinant of the scattering matrix is related to the total number of bound states including the multiplicities.

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Inverse Scattering,om a given scattering matrix without having the bound-state information. From the given scattering matrix alone we show how to construct a scattering data set belonging to the Marchenko class so that the constructed scattering data set can be used as input into a properly posed inverse scattering pr