scholarly journals Trace formulas for the matrix Schrödinger operator on the half-line with general boundary conditions

2016 ◽  
Vol 57 (11) ◽  
pp. 112101 ◽  
Author(s):  
Ricardo Weder
Keyword(s):  
Boundary Conditions ◽  
Schrödinger Operator ◽  
General Boundary ◽  
Half Line ◽  
Schrodinger Operator ◽  
General Boundary Conditions ◽  
Trace Formulas ◽  
The Matrix

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.

Sign in / Sign up

Export Citation Format

Share Document