Asymptotic expansion of the scattering matrix associated with matrix Schrödinger operator

2012 ◽  
Vol 80 (1-2) ◽  
pp. 57-78 ◽  
Author(s):  
Hamadi Baklouti ◽  
Slaheddine Ben Abdeljeilil
Keyword(s):  
Asymptotic Expansion ◽  
Schrödinger Operator ◽  
Scattering Matrix ◽  
Schrodinger Operator

A star-graph model via operator extension

2007 ◽  
Vol 142 (2) ◽  
pp. 365-384 ◽  
Author(s):  
B. PAVLOV
Keyword(s):  
Schrödinger Operator ◽  
Quantum Wires ◽  
Graph Model ◽  
Scattering Matrix ◽  
Quantum Graph ◽  
Spectral Interval ◽  
Star Graph ◽  
Quantum Network ◽  
Schrodinger Operator ◽  
One Dimensional

AbstractOne usually assumes that the Schrödinger operator on a thin quantum network (“fattened graph”) can be simulated by the ordinary Schrödinger operator on the corresponding one-dimensional quantum graph. On the other hand, each quantum graph can be constructed of standard elements – star graphs. We prove that a thin star-shaped quantum network which consists of a compact domain and a few straight semi-infinite quantum wires, with a two-dimensional Schrödinger operator on it, can be simulated by the corresponding solvable model in form of a one-dimensional star graph: an outer space, with an ordinary Schrödinger operator on the leads, a resonance vertex supplied with an inner space and a finite matrix in it and an appropriate boundary condition connecting the inner and outer components of elements from the domain of the model. The model is (locally) quantitatively consistent: the scattering matrix of the model on a certain spectral interval serves an approximation of the scattering matrix of the network. The role of the constructed star-graph model as a “jump-start” in analytic perturbation procedure on continuous spectrum is discussed.

Inverse scattering for the higher order Schrödinger operator with a first order perturbation

2019 ◽  
Vol 27 (3) ◽  
pp. 409-427
Author(s):  
Hua Huang ◽  
Zhiwen Duan ◽  
Quan Zheng
Keyword(s):  
Inverse Scattering ◽  
Schrödinger Operator ◽  
Scattering Matrix ◽  
Higher Order ◽  
Zero Order ◽  
Schrodinger Operator ◽  
Scattering Problems ◽  
First Order ◽  
Fixed Energy ◽  
First Order Perturbation

Abstract This paper concerns inverse scattering problems at a fixed energy for the higher order Schrödinger operator with the first order perturbed potentials in dimensions {n\geq 3} . We show that the scattering matrix uniquely determines the first order perturbed potentials and the zero order potentials.

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