Modified Hamiltonian systems and canonical transformations arising from the relationship between generalized Zakharov–Shabat and energy‐dependent Schrödinger operators

1981 ◽  
Vol 22 (11) ◽  
pp. 2497-2503 ◽  
Author(s):  
L. Martínez Alonso ◽  
F. Guil Guerrero
Keyword(s):  
Hamiltonian Systems ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Canonical Transformations ◽  
Energy Dependent ◽  
The Relationship

scholarly journals QUASI-EXACTLY SOLVABLE MATRIX SCHRÖDINGER OPERATORS

2000 ◽  
Vol 15 (26) ◽  
pp. 1647-1653 ◽  
Author(s):  
YVES BRIHAYE
Keyword(s):  
Polynomial Matrix ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Lamé Equation ◽  
Matrix Potential ◽  
Exactly Solvable ◽  
The Relationship

Two families of quasi-exactly solvable 2×2 matrix Schrödinger operators are constructed. The first one is based on a polynomial matrix potential and depends on three parameters. The second is a one-parameter generalization of the scalar Lamé equation. The relationship between these operators and QES Hamiltonians already considered in the literature is pointed out.

Identities for Eigenvalues of the Schrödinger Equation with Energy-Dependent Potential

2011 ◽  
Vol 66 (12) ◽  
pp. 699-704 ◽  
Author(s):  
Chuan Fu Yang
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Eigenvalue Problems ◽  
Schrödinger Operators ◽  
Contour Integration ◽  
Schrodinger Operators ◽  
Separated Boundary Conditions ◽  
Dependent Potential ◽  
Energy Dependent

The present paper deals with eigenvalue problems for the Schrödinger equation with energy dependent potential and some separated boundary conditions. Using the method of contour integration, we obtain some new regularized traces for this class of Schrödinger operators.

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