The generalized star product and the factorization of scattering matrices on graphs
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Publication:2774851
DOI10.1063/1.1354641zbMath1053.81087arXivmath-ph/0008022OpenAlexW2017038138MaRDI QIDQ2774851
Vadim Kostrykin, Robert Schrader
Publication date: 26 February 2002
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0008022
PDEs in connection with quantum mechanics (35Q40) (S)-matrix theory, etc. in quantum theory (81U20) Scattering theory, inverse scattering involving ordinary differential operators (34L25)
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Cites Work
- Scattering problems on noncompact graphs
- Symmetries of Schrödinger operators with point interactions
- Evanescent modes in a multiple scattering factorization
- Distribution theory for discontinuous test functions and differential operators with generalized coefficients
- Global bounds for the Lyapunov exponent and the integrated density of states of random Schrödinger operators in one dimension
- Kirchhoff's Rule for Quantum Wires. II: The Inverse Problem with Possible Applications to Quantum Computers
- On the Relation of Transmission-Line Theory to Scattering and Transfer
- A factorization of the scattering matrix for the Schrödinger equation and for the wave equation in one dimension
- Inverse scattering on the line
- Cluster Properties of One Particle Schrödinger Operators. II
- Contact interactions on graph superlattices
- Inverse eigenvalue problems on directed graphs
- Kirchhoff's rule for quantum wires
- SCATTERING THEORY APPROACH TO RANDOM SCHRÖDINGER OPERATORS IN ONE DIMENSION
- Periodic Schrödinger operators with large gaps and Wannier-Stark ladders
- CLUSTER PROPERTIES OF ONE PARTICLE SCHRÖDINGER OPERATORS
- THE DENSITY OF STATES AND THE SPECTRAL SHIFT DENSITY OF RANDOM SCHRÖDINGER OPERATORS
- Four-parameter point-interaction in 1D quantum systems
- On the number of states bound by one-dimensional finite periodic potentials
- NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING
- Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation
