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Schrodinger Operators
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Book Synopsis Mathematical Methods in Quantum Mechanics by : Gerald Teschl
Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2009 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).
Book Synopsis Schrödinger Operators by : Hans L. Cycon
Download or read book Schrödinger Operators written by Hans L. Cycon and published by Springer Science & Business Media. This book was released on 1987 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are you looking for a concise summary of the theory of Schrödinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don’t just cover general properties, but also detail multiparticle quantum mechanics – including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years.
Book Synopsis Spectral Theory of Random Schrödinger Operators by : R. Carmona
Download or read book Spectral Theory of Random Schrödinger Operators written by R. Carmona and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous.
Book Synopsis Introduction to Spectral Theory by : P.D. Hislop
Download or read book Introduction to Spectral Theory written by P.D. Hislop and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.
Book Synopsis Products of Random Matrices with Applications to Schrödinger Operators by : P. Bougerol
Download or read book Products of Random Matrices with Applications to Schrödinger Operators written by P. Bougerol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: CHAPTER I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. The difference equation. Hyperbolic structures 187 2. Self adjointness of H. Spectral properties . 190 3. Slowly increasing generalized eigenfunctions 195 4. Approximations of the spectral measure 196 200 5. The pure point spectrum. A criterion 6. Singularity of the spectrum 202 CHAPTER II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. General spectral properties 206 3. The Lyapunov exponent in the general ergodie case 209 4. The Lyapunov exponent in the independent eas e 211 5. Absence of absolutely continuous spectrum 221 224 6. Distribution of states. Thouless formula 232 7. The pure point spectrum. Kotani's criterion 8. Asymptotic properties of the conductance in 234 the disordered wire CHAPTER III THE PURE POINT SPECTRUM 237 238 1. The pure point spectrum. First proof 240 2. The Laplace transform on SI(2,JR) 247 3. The pure point spectrum. Second proof 250 4. The density of states CHAPTER IV SCHRÖDINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schrödinger operator in 253 a strip 259 2. Ergodie Schrödinger operators in a strip 3. Lyapunov exponents in the independent case. 262 The pure point spectrum (first proof) 267 4. The Laplace transform on Sp(~,JR) 272 5. The pure point spectrum, second proof vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This book presents two elosely related series of leetures. Part A, due to P.
Book Synopsis Schrödinger Operators, Spectral Analysis and Number Theory by : Sergio Albeverio
Download or read book Schrödinger Operators, Spectral Analysis and Number Theory written by Sergio Albeverio and published by Springer Nature. This book was released on 2021-06-03 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrödinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.
Book Synopsis Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158) by : Jean Bourgain
Download or read book Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158) written by Jean Bourgain and published by Princeton University Press. This book was released on 2005 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations. Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."
Book Synopsis Spectral Theory of Schrodinger Operators by : Rafael del Río
Download or read book Spectral Theory of Schrodinger Operators written by Rafael del Río and published by American Mathematical Soc.. This book was released on 2004 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the articles based on a series of lectures from a workshop held at the Institute of Applied Mathematics of the National University of Mexico. The aim of the book is to present to a non-specialized audience the basic tools needed to understand and appreciate new trends of research on Schrodinger operator theory. Topics discussed include various aspects of the spectral theory of differential operators, the theory of self-adjoint operators, finite rank perturbations, spectral properties of random Schrodinger operators, and scattering theory for Schrodinger operators. The material is suitable for graduate students and research mathematicians interested in differential operators, in particular, spectral theory of Schrodinger operators.
Book Synopsis Schrödinger Operators, Como 1984 by : Sandro Graffi
Download or read book Schrödinger Operators, Como 1984 written by Sandro Graffi and published by Springer. This book was released on 2006-11-14 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis One-Dimensional Ergodic Schrödinger Operators by : David Damanik
Download or read book One-Dimensional Ergodic Schrödinger Operators written by David Damanik and published by American Mathematical Society. This book was released on 2022-08-18 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks. Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrödinger operators with dynamically defined potentials. It also includes a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics. This text is accessible to graduate students who have completed one-semester courses in measure theory and complex analysis. It is intended to serve as an introduction to the field for junior researchers and beginning graduate students as well as a reference text for people already working in this area. It is well suited for self-study and contains numerous exercises (many with hints).
Book Synopsis Schrödinger Operators, Aarhus 1985 by : Erik Balslev
Download or read book Schrödinger Operators, Aarhus 1985 written by Erik Balslev and published by Springer. This book was released on 2006-11-14 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities by : Rupert L. Frank
Download or read book Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities written by Rupert L. Frank and published by Cambridge University Press. This book was released on 2022-11-17 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students, and includes an ample amount of background material on the spectral theory of linear operators in Hilbert spaces and on Sobolev space theory. Of particular interest is a family of inequalities by Lieb and Thirring on eigenvalues of Schrödinger operators, which they used in their proof of stability of matter. The final part of this book is devoted to the active research on sharp constants in these inequalities and contains state-of-the-art results, serving as a reference for experts and as a starting point for further research.
Book Synopsis Spectral Representations for Schrödinger Operators with Long-Range Potentials by : Yoshimi Saito
Download or read book Spectral Representations for Schrödinger Operators with Long-Range Potentials written by Yoshimi Saito and published by Springer. This book was released on 2006-11-15 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Schrödinger Operators The Quantum Mechanical Many-Body Problem by : Erik Balslev
Download or read book Schrödinger Operators The Quantum Mechanical Many-Body Problem written by Erik Balslev and published by Springer. This book was released on 2005-08-11 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these proceedings basic questions regarding n-body Schr|dinger operators are dealt with, such as asymptotic completeness of systems with long-range potentials (including Coulomb), a new proof of completeness for short-range potentials, energy asymptotics of large Coulomb systems,asymptotic neutrality of polyatomic molecules. Other contributions deal withdifferent types of problems, such as quantum stability, Schr|dinger operators on a torus and KAM theory, semiclassical theory, time delay, radiation conditions, magnetic Stark resonances, random Schr|dinger operators and stochastic spectral analysis. The volume presents the results in such detail that it could well serve as basic literature for seminar work.
Book Synopsis The d-bar Neumann Problem and Schrödinger Operators by : Friedrich Haslinger
Download or read book The d-bar Neumann Problem and Schrödinger Operators written by Friedrich Haslinger and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-09-18 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book's subject lies in the nexus of partial differential equations, operator theory, and complex analysis. The spectral analysis of the complex Laplacian and the compactness of the d-bar-Neumann operator are primary topics.The revised 2nd edition explores updates to Schrödinger operators with magnetic fields and connections to the Segal Bargmann space (Fock space), to quantum mechanics, and the uncertainty principle.
Book Synopsis Topics in the Theory of Schrödinger Operators by : Huzihiro Araki
Download or read book Topics in the Theory of Schrödinger Operators written by Huzihiro Araki and published by World Scientific. This book was released on 2004-05-07 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents reviews of some recent topics in the theory of Schrödinger operators. It includes a short introduction to the subject, a survey of the theory of the Schrödinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion) with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli–Fierz model with the use of the functional integral. The material is accessible to graduate students and non-expert researchers. Contents: Time-Periodic Schrödinger Equations (K Yajima)An Application of Phase Space Tunneling to Multistate Scattering Theory (A Martinez et al.)Inverse Spectral Theory (H Isozaki)Analysis of Ground States of Atoms Interacting with a Quantized Radiation Field (F Hiroshima) Readership: Researchers and graduate students in mathematical physics, high energy physics, theoretical physics, and analysis and differential equations. Keywords:Schrödinger Operator;Time-Periodic Potential;Scattering Theory;Coherent State Expansion;Semi-Classical Limit of the S-Matrix;Inverse Problems;PauliâFierz Model;Functional Integral
Book Synopsis Topics in the Theory of Schrödinger Operators by : Huzihiro Araki
Download or read book Topics in the Theory of Schrödinger Operators written by Huzihiro Araki and published by World Scientific. This book was released on 2004 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents reviews of some recent topics in thetheory of SchrAdinger operators. It includes a short introduction tothe subject, a survey of the theory of the SchrAdinger equation whenthe potential depends on the time periodically, an introduction to theso-called FBI transformation (also known as coherent state expansion)with application to the semi-classical limit of the S-matrix, anoverview of inverse spectral and scattering problems, and a study ofthe ground state of the PauliOCoFierz model with the use of thefunctional integral. The material is accessible to graduate studentsand non-expert researchers."
