Dimensional Hausdorff properties of singular continuous spectra [PDF]
, 1995 We present an extension of the Gilbert-Pearson theory of subordinacy, which relates dimensional Hausdorff spectral properties of one-dimensional Schrödinger operators to the behavior of solutions of the corresponding Schrödinger equation.
Jitomirskaya, Svetlana Ya., Last, Yoram
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Kato's inequality for magnetic relativistic Schrödinger operators [PDF]
, 2016 Kato’s inequality is shown for the magnetic relativistic Schrödinger operator HA, m defined as the operator theoretical square root of the self adjoint, magnetic nonrelativistic Schrödinger operator (−i∇ − A(x))2 + m2 with L 2 loc vector potential A(x)
Fumio Hiroshima (7160015) +2 more
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Some Spectral Properties of Schrödinger Operators on Semi Axis
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 The main aim of this work is to investigate some spectral properties of Schrödinger operators on semi axis. We first present the Schrödinger equation with a piecewise continuous potential function q so that the problem differs from the classical ...
İbrahim Erdal
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Schrödinger operators with δ and δ′-potentials supported on hypersurfaces [PDF]
, 2012 Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions.
A. Posilicano +57 more
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Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential [PDF]
Communications in Mathematical Physics, 2012 We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage ...
Katsiaryna Krupchyk, G. Uhlmann
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Nonlinear conservation laws for the Schrödinger boundary value problems of second order
Boundary Value Problems, 2020 In this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order.
Ming Ren, Shiwei Yun, Zhenping Li
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Spectral properties of periodic systems cut at an angle
Comptes Rendus. Mathématique, 2021 We consider a semi-periodic two-dimensional Schrödinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure.
Gontier, David
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Accurate Semiclassical Spectral Asymptotics for a Two-Dimensional Magnetic Schrödinger Operator [PDF]
, 2013 We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schrödinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value b0 of the intensity of the magnetic field is strictly positive, and the ...
B. Helffer, Y. Kordyukov
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A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum
Advances in Mathematical Physics, 2016 We consider the nonlinear Schrödinger equation -Δu+f(u)=V(x)u in RN. The potential function V satisfies that the essential spectrum of the Schrödinger operator -Δ-V is [0,+∞) and this Schrödinger operator has infinitely many negative eigenvalues ...
Shaowei Chen, Haijun Zhou
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Discrete Schrödinger operators and Finsler metric (Spectral and Scattering Theory and Related Topics) [PDF]
, 2023 In this article, we review the results in [9] on the Agmon estimate for discrete Schrödinger operators. We first discuss the semiclassical analysis for discrete Schrödinger operators with emphasis on the microlocal analysis on the torus.
Kameoka, Kentaro
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