Schrödinger operators in the twentieth century

Barry Simon

Type: Article

Publication Date: 2000-06-01

Citations: 131

DOI: https://doi.org/10.1063/1.533321

Abstract

This paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics.

Locations

Journal of Mathematical Physics - View
CiteSeer X (The Pennsylvania State University) - View - PDF
CaltechAUTHORS (California Institute of Technology) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Schrödinger Operators	2020	David Borthwick
+	Review: Martin Schechter, Operator methods in quantum mechanics	1982	William G. Faris
+ PDF Chat	Spectral Theory of Schrödinger Operators	2004	Rafael del RÃo Carlos Villegas‐Blas
+	Schrödinger operators	1995	E. B. Davies
+	Operator Hilbert-Space Methodology in Quantum Physics	2009
+	書評 Gerald Teschl : Mathematical Methods in Quantum Mechanics : With Applications to Schrodinger Operators	2013	裕昭新國
+	Mathematical Methods in Quantum Mechanics	2009	Gerald Teschl
+	Mathematics for Quantum Mechanics: An Introductory Survey of Operators, Eigenvalues, and Linear Vector Spaces	2006	John David Jackson
+ PDF Chat	Book Review: Hilbert space operators in quantum physics	1995	William G. Faris
+ PDF Chat	Resonance Theory for Schrödinger Operators	2001	Ovidiu Costin Avy Soffer
+	Spectral Calculus for Schrödinger Operators	2009	Shijun Zheng
+	Schrödinger equation in higher dimensions	2012
+	Spectral Calculus for Schrödinger Operators in One and Three Dimensions	2006	Shijun Zheng
+	Schrödinger’s Wave Mechanics	2012	Alexander Komech
+	Operator methods in quantum mechanics	1981	Martin Schechter
+	Non‐Selfadjoint Operators in Quantum Physics	2015	Фабио Багарелло Jean‐Pierre Gazeau Franciszek Hugon Szafraniec Miloslav Znojil
+ PDF Chat	Discovery of the relativistic Schrödinger equation	2021	Kamal Barley José Vega-Guzmán Andreas Ruffing Sergeĭ K. Suslov
+	Spectral theory and wave operators for the Schrödinger equation	1982	A. M. Berthier
+	The Spectra of Quantum-Mechanical Operators	1952	C. R. Putnam
+	Recent Developments in Spectral Theory for Non-self-adjoint Hamiltonians	2024	Lucrezia Cossetti Luca Fanelli Nico Michele Schiavone

Works That Cite This (102)

Action	Title	Year	Authors
+ PDF Chat	Finite propagation speed and kernel estimates for Schrödinger operators	2007	Christian Remling
+	Variational Problems in Molecular Simulation	2015	MariaJ. Esteban
+	Spectral invariants of the magnetic Dirichlet-to-Neumann map on Riemannian manifolds	2023	Genqian Liu Xiaoming Tan
+ PDF Chat	Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations	2005	Atanas Stefanov P. G. Kevrekidis
+ PDF Chat	Bounds on the density of states for Schrödinger operators	2012	Jean Bourgain Abel Klein
+ PDF Chat	Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation	2008	Alexander Sakhnovich
+ PDF Chat	Существенная самосопряженность операторов типа Шрeдингера на многообразиях	2002	Михаил Ш Браверман Михаил Ш Браверман О Милатович Ognjen Milatovic Mikhail Shubin Mikhail Shubin
+ PDF Chat	Schrödinger equation and the oscillatory semigroup for the Hermite operator	2005	A. K. Nandakumaran P. K. Ratnakumar
+ PDF Chat	On the spectral L2 conjecture, 3/2-Lieb-Thirring inequality and distributional potentials	2005	Alexei Rybkin
+ PDF Chat	Topics from spectral theory of differential operators	2004	Andréas Hinz

Works Cited by This (205)

Action	Title	Year	Authors
+	Semiclassical analysis of low lying eigenvalues. I. Non-degenerate minima : asymptotic expansions	1983	Barry Simon
+	WEAKLY-BOUND STATES OF 3 RESONANTLY-INTERACTING PARTICLES	1971	V.N. Efimov
+	Characterization of bound states and scattering states in quantum mechanics	1973	Werner O. Amrein Vladimir Georgescu
+	Spectral Analysis of Multiparticle Schrödinger Operators	1981	Barry Simon
+	Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems	1981	René Carmona Barry Simon
+	Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results	1998	Michael Christ Alexander Kiselev
+	Inverse Problems in Quantum Scattering Theory	1977	Khosrow Chadan Pierre Sabatier
+	Almost periodic Schrödinger operators II. The integrated density of states	1983	J. E. Avron Barry Simon
+	Semiclassical quantum mechanics	1980	George A. Hagedorn
+	Scattering Theory of Classical and Quantum N-Particle Systems	1997	Jan Dereziński Christian Gérard