Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general self-adjoint boundary conditions

DOI10.1017/S1446181100008014zbMath1017.34085arXivmath-ph/0703007OpenAlexW2103359496MaRDI QIDQ3146206

M. S. Harmer

Publication date: 11 September 2002

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0703007

zbMATH Keywords

Darboux transformationoperator on graphsmatrix Schrödinger operatorselfadjoint boundary and Lagrange plane

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (22)

A matrix Schrödinger approach to focusing nonlinear Schrödinger equations with nonvanishing boundary conditions ⋮ Symmetries of quantum graphs and the inverse scattering problem ⋮ Scattering theory for the matrix Schrödinger operator on the half line with general boundary conditions ⋮ Determination of the self-adjoint matrix Schrödinger operators without the bound state data ⋮ The number of eigenvalues of the matrix Schrödinger operator on the half line with general boundary conditions ⋮ Recovering the shape of a quantum graph ⋮ Stability of the inverse scattering problem for the self‐adjoint matrix Schrödinger operator on the half line ⋮ From the AKNS system to the matrix Schrödinger equation with vanishing potentials: Direct and inverse problems ⋮ Some inverse scattering problems on star-shaped graphs ⋮ Spectral data characterization for the Sturm-Liouville operator on the star-shaped graph ⋮ Inverse problems for Aharonov–Bohm rings ⋮ High-energy analysis and Levinson's theorem for the selfadjoint matrix Schrödinger operator on the half line ⋮ Inverse problem solution and spectral data characterization for the matrix Sturm-Liouville operator with singular potential ⋮ Small-energy analysis for the selfadjoint matrix Schrödinger operator on the half line. II ⋮ \(L^p-L^{p'}\) estimates for matrix Schrödinger equations ⋮ Inverse scattering problems on a noncompact star graph ⋮ Trace formulas for Schrödinger operators on star graphs with general matching conditions ⋮ Direct and inverse problems for the matrix Sturm-Liouville operator with general self-adjoint boundary conditions ⋮ Trace formulas for the matrix Schrödinger operator on the half-line with general boundary conditions ⋮ Constructive solution of the inverse spectral problem for the matrix Sturm–Liouville operator ⋮ Small-energy analysis for the self-adjoint matrix Schrödinger operator on the half line ⋮ The spectral shift function and Levinson's theorem for quantum star graphs

Cites Work

• Kirchhoff's rule for quantum wires
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