scholarly journals Inverse problems for selfadjoint Schrödinger operators on the half line with compactly supported potentials

2015 ◽  
Vol 56 (2) ◽  
pp. 022106 ◽  
Author(s):  
Tuncay Aktosun ◽  
Paul Sacks ◽  
Mehmet Unlu
Keyword(s):  
Inverse Problems ◽  
Schrödinger Operators ◽  
Half Line ◽  
Schrodinger Operators ◽  
Compactly Supported

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 Wegner estimate for discrete Schrödinger operators with Gaussian random potentials

2019 ◽  
Vol 27 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Martin Tautenhahn
Keyword(s):  
Conditional Distribution ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Gaussian Random Process ◽  
Random Potentials ◽  
Wegner Estimate ◽  
Compactly Supported ◽  
Covariance Functions ◽  
Monotonicity Assumption ◽  
Discrete Schrödinger Operators

Abstract We prove a Wegner estimate for discrete Schrödinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially; no monotonicity assumption is required. This improves earlier results where abstract conditions on the conditional distribution, compactly supported and non-negative, or compactly supported covariance functions with positive mean are considered.

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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