scholarly journals A Sharp Bound on Eigenvalues of Schrödinger Operators on the Half-line with Complex-valued Potentials

2011 ◽  
pp. 39-44 ◽  
Author(s):  
Rupert L. Frank ◽  
Ari Laptev ◽  
Robert Seiringer
Keyword(s):  
Schrödinger Operators ◽  
Sharp Bound ◽  
Half Line ◽  
Schrodinger Operators ◽  
Complex Valued

scholarly journals A characterization of singular Schrödinger operators on the half-line

2020 ◽  
pp. 1-19
Author(s):  
Raffaele Scandone ◽  
Lorenzo Luperi Baglini ◽  
Kyrylo Simonov
Keyword(s):  
Schrödinger Operators ◽  
Half Line ◽  
Schrodinger Operators

scholarly journals Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials

2006 ◽  
Vol 77 (3) ◽  
pp. 309-316 ◽  
Author(s):  
Rupert L. Frank ◽  
Ari Laptev ◽  
Elliott H. Lieb ◽  
Robert Seiringer
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Complex Valued

scholarly journals Bounds for Schrödinger Operators on the Half-Line Perturbed by Dissipative Barriers

2021 ◽  
Vol 93 (6) ◽  
Author(s):  
Alexei Stepanenko
Keyword(s):  
Schrödinger Operators ◽  
Half Line ◽  
Schrodinger Operators ◽  
Maximum Magnitude

AbstractWe consider Schrödinger operators of the form $$H_R = - \,\text {{d}}^2/\,\text {{d}}x^2 + q + i \gamma \chi _{[0,R]}$$ H R = - d 2 / d x 2 + q + i γ χ [ 0 , R ] for large $$R>0$$ R > 0 , where $$q \in L^1(0,\infty )$$ q ∈ L 1 ( 0 , ∞ ) and $$\gamma > 0$$ γ > 0 . Bounds for the maximum magnitude of an eigenvalue and for the number of eigenvalues are proved. These bounds complement existing general bounds applied to this system, for sufficiently large R.

The analytic structure of the reflection coefficient, a sum rule and a complete description of the Weyl m-function of half-line Schrödinger operators with L2-type potentials

2006 ◽  
Vol 136 (3) ◽  
pp. 615-632 ◽  
Author(s):  
Alexei Rybkin
Keyword(s):  
Reflection Coefficient ◽  
Schrödinger Operators ◽  
Half Line ◽  
Analytic Structure ◽  
Schrodinger Operators ◽  
Trace Inequality ◽  
Sum Rule ◽  
One Dimensional ◽  
Upper Half Plane ◽  
Image Position

We prove that the reflection coefficient of one-dimensional Schrödinger operators with potentials supported on a half-line can be represented in the upper half-plane as the quotient of a contractive analytic function and a properly regularized Blaschke product. We apply this fact to obtain a new trace formula and trace inequality for the reflection coefficient that yields a description of the Weyl m-function of Dirichlet half-line Schrödinger operators with slowly decaying potentials q subject to Among others, we also refine the 3/2-Lieb-Thirring inequality.

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