scholarly journals Erratum: The number of eigenvalues of the matrix Schrödinger operator on the half line with general boundary conditions [J. Math. Phys. 58, 102107 (2017)]

2019 ◽  
Vol 60 (1) ◽  
pp. 019902
Author(s):  
Ricardo Weder
Keyword(s):  
Boundary Conditions ◽  
Schrödinger Operator ◽  
General Boundary ◽  
Half Line ◽  
Schrodinger Operator ◽  
General Boundary Conditions ◽  
The Matrix ◽  
Math Phys

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.

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