scholarly journals Asymptotic behaviour of resonance eigenvalues of the Schrödinger operator with a matrix potential

2020 ◽  
Vol 69 (1) ◽  
pp. 486-510
Author(s):  
Setenay Akduman ◽  
Sedef Karakılıç ◽  
Didem Coşkan
Keyword(s):  
Asymptotic Behaviour ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Matrix Potential

Spectral gaps of the Schrödinger operators with periodic δ′-interactions and Diophantine approximations

2007 ◽  
Vol 143 (1) ◽  
pp. 185-199
Author(s):  
KAZUSHI YOSHITOMI
Keyword(s):  
Asymptotic Behaviour ◽  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Spectral Gaps ◽  
Diophantine Approximations ◽  
Image Position ◽  
Markov Constant

AbstractWe study the spectral gaps of the Schrödinger operatorwhere κ∈(0,2π) and$\beta_{1},\beta_{2}\in{\mathbb R}\setminus\{0\}$are parameters. Let τ=2π−κ. Suppose that the ratio κ0:=τ/κ is irrational. We denote thejth gap of the spectrum ofHbyGj, its length by |Gj|. We obtain a relationship between the asymptotic behaviour of |Gj| asj→∞ and the Diophantine properties of κ0. In particular, we show that if β1+β2=0, thenwhereM(κ0) stands for the Markov constant of κ0.

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

2002 ◽  
Vol 44 (1) ◽  
pp. 161-168 ◽  
Author(s):  
M. S. Harmer
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Inverse Scattering ◽  
Darboux Transformation ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
General Boundary Conditions ◽  
Matrix Potential ◽  
The Matrix ◽  
Marchenko Equation

AbstractUsing a parameterisation of general self-adjoint boundary conditions in terms of Lagrange planes we propose a scheme for factorising the matrix Schrödinger operator and hence construct a Darboux transformation, an interesting feature of which is that the matrix potential and boundary conditions are altered under the transformation. We present a solution of the inverse problem in the case of general boundary conditions using a Marchenko equation and discuss the specialisation to the case of a graph with trivial compact part, that is, with diagonal matrix potential.

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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