scholarly journals On the Schrödinger operator with a periodic PT-symmetric matrix potential

2021 ◽  
Vol 62 (10) ◽  
pp. 103501
Author(s):  
O. A. Veliev
Keyword(s):  
Schrödinger Operator ◽  
Symmetric Matrix ◽  
Schrodinger Operator ◽  
Matrix Potential

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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