Reflection Probabilities of One-Dimensional Schrödinger Operators and Scattering Theory

Annales Henri Poincaré ◽

10.1007/s00023-016-0543-0 ◽

2017 ◽

Vol 18 (6) ◽

pp. 2075-2085 ◽

Author(s):

Benjamin Landon ◽

Annalisa Panati ◽

Jane Panangaden ◽

Justine Zwicker

Keyword(s):

Scattering Theory ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

One Dimensional

Download Full-text

Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials

Journal d Analyse Mathématique ◽

10.1007/s11854-008-0050-4 ◽

2008 ◽

Vol 106 (1) ◽

pp. 271-316 ◽

Author(s):

Anne Boutet de Monvel ◽

Iryna Egorova ◽

Gerald Teschl

Keyword(s):

Inverse Scattering ◽

Scattering Theory ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

One Dimensional ◽

Inverse Scattering Theory

Download Full-text

Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions

Communications in Mathematical Physics ◽

10.1007/bf02097231 ◽

1993 ◽

Vol 158 (1) ◽

pp. 45-66 ◽

Author(s):

Anton Bovier ◽

Jean-Michel Ghez

Keyword(s):

Spectral Properties ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

One Dimensional

Download Full-text

Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials

Journal of Functional Analysis ◽

10.1016/j.jfa.2008.07.015 ◽

2008 ◽

Vol 255 (9) ◽

pp. 2321-2362 ◽

Author(s):

Ovidiu Costin ◽

Wilhelm Schlag ◽

Wolfgang Staubach ◽

Saleh Tanveer

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Semiclassical Analysis ◽

Zero Energy ◽

One Dimensional ◽

Energy Scattering ◽

Inverse Square Potentials

Download Full-text

Bounds for the Points of Spectral Concentration of One-dimensional Schrödinger Operators

Spectral Methods for Operators of Mathematical Physics ◽

10.1007/978-3-0348-7947-7_8 ◽

2004 ◽

pp. 139-149

Author(s):

Daphne J. Gilbert ◽

Bernard J. Harris ◽

Suzanne M. Riehl

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

One Dimensional ◽

Spectral Concentration

Download Full-text

One Dimensional Schrödinger Operators

Spectral and Scattering Theory for Second-Order Partial Differential Operators ◽

10.1201/9781315152905-8 ◽

2017 ◽

pp. 113-134

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

One Dimensional

Download Full-text

Embedded singular continuous spectrum for one-dimensional Schrödinger operators

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-99-02495-2 ◽

1999 ◽

Vol 351 (6) ◽

pp. 2479-2497 ◽

Author(s):

Christian Remling

Keyword(s):

Continuous Spectrum ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

Singular Continuous Spectrum ◽

One Dimensional

Download Full-text

A power series analysis of bound and resonance states of one-dimensional Schrödinger operators with finite point interactions

Applied Mathematics and Computation ◽

10.1016/j.amc.2021.126774 ◽

2022 ◽

Vol 417 ◽

pp. 126774

Author(s):

Víctor Barrera-Figueroa

Keyword(s):

Power Series ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

Point Interactions ◽

Finite Point ◽

Resonance States ◽

One Dimensional ◽

Series Analysis

Download Full-text

The Exact Number of Eigenvalues of the Discrete Schrödinger Operators in One-Dimensional Case

Lobachevskii Journal of Mathematics ◽

10.1134/s1995080221060172 ◽

2021 ◽

Vol 42 (6) ◽

pp. 1294-1303

Author(s):

S. N. Lakaev ◽

I. U. Alladustova

Keyword(s):

Schrödinger Operators ◽

Dimensional Case ◽

Schrodinger Operators ◽

One Dimensional ◽

Exact Number ◽

Discrete Schrödinger Operators

Download Full-text

Spectral and Scattering Theory for Schrodinger Operators with Potentials Independent of | x |

American Journal of Mathematics ◽

10.2307/2374837 ◽

1991 ◽

Vol 113 (3) ◽

pp. 509 ◽

Author(s):

Ira W. Herbst

Keyword(s):

Scattering Theory ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

Spectral And Scattering Theory

Download Full-text

PACKING SUBORDINACY WITH APPLICATION TO SPECTRAL CONTINUITY

Journal of the Australian Mathematical Society ◽

10.1017/s1446788719000193 ◽

2019 ◽

Vol 108 (2) ◽

pp. 226-244 ◽

Author(s):

V. R. BAZAO ◽

S. L. CARVALHO ◽

C. R. DE OLIVEIRA

Keyword(s):

Continuous Spectrum ◽

Dimensional Stability ◽

Schrödinger Operators ◽

Stability Result ◽

Schrodinger Operators ◽

Spectral Measures ◽

One Dimensional ◽

Continuity Properties ◽

Rotation Numbers ◽

Spectral Continuity

By using methods of subordinacy theory, we study packing continuity properties of spectral measures of discrete one-dimensional Schrödinger operators acting on the whole line. Then we apply these methods to Sturmian operators with rotation numbers of quasibounded density to show that they have purely $\unicode[STIX]{x1D6FC}$-packing continuous spectrum. A dimensional stability result is also mentioned.

Download Full-text