Topics In The Theory Of Schr Dinger Operators
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Topics In The Theory Of Schrodinger Operators
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Author : Huzihiro Araki
language : en
Publisher: World Scientific
Release Date : 2004
Topics In The Theory Of Schrodinger Operators written by Huzihiro Araki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Medical categories.
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."
Schr Dinger Operators
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Author : Hans L. Cycon
language : en
Publisher: Springer
Release Date : 2009-08-19
Schr Dinger Operators written by Hans L. Cycon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-19 with Science categories.
A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem.
Topics In The Theory Of Schrodinger Operators
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Author : Huzihiro Araki
language : en
Publisher: World Scientific
Release Date : 2004-05-07
Topics In The Theory Of Schrodinger Operators written by Huzihiro Araki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-07 with Science categories.
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.
Introduction To Spectral Theory
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Author : P.D. Hislop
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Spectral Theory written by P.D. Hislop and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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.
Spectral Theory Of Schrodinger Operators
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Author : Rafael del Río
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Spectral Theory Of Schrodinger Operators written by Rafael del Río and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Quantum Theory For Mathematicians
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Author : Brian C. Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-19
Quantum Theory For Mathematicians written by Brian C. Hall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-19 with Science categories.
Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
Mathematical Methods In Quantum Mechanics
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Author : Gerald Teschl
language : en
Publisher:
Release Date : 2009
Mathematical Methods In Quantum Mechanics written by Gerald Teschl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Quantum theory categories.
Products Of Random Matrices With Applications To Schrodinger Operators
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Author : P. Bougerol
language : en
Publisher:
Release Date : 2014-01-15
Products Of Random Matrices With Applications To Schrodinger Operators written by P. Bougerol and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Self Adjoint Extensions In Quantum Mechanics
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Author : D.M. Gitman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-27
Self Adjoint Extensions In Quantum Mechanics written by D.M. Gitman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-27 with Science categories.
This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert spaces. The authors begin by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes to the naive treatment. It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems. In the end, related problems in quantum field theory are briefly introduced. This well-organized text is most suitable for students and post graduates interested in deepening their understanding of mathematical problems in quantum mechanics. However, scientists in mathematical and theoretical physics and mathematicians will also find it useful.
One Dimensional Ergodic Schr Dinger Operators
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Author : David Damanik
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-15
One Dimensional Ergodic Schr Dinger Operators written by David Damanik and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-15 with Mathematics categories.
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. The current volume addresses specific classes of operators, including the important examples of random and almost-periodic operators. The text serves as a self-contained introduction to the field for junior researchers and beginning graduate students, as well as a reference text for people already working in this area. The general theory of one-dimensional ergodic operators was presented in the book by the same authors as volume 221 in the Graduate Studies in Mathematics series.