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Lecture Notes On Schr Dinger Equations


Lecture Notes On Schr Dinger Equations
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Lecture Notes On Schr Dinger Equations


Lecture Notes On Schr Dinger Equations
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Author : Aleksandr Andreevich Pankov
language : en
Publisher:
Release Date : 2007

Lecture Notes On Schr Dinger Equations written by Aleksandr Andreevich Pankov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.


CONTENTS: Preface; A Bit of Quantum Mechanics; Operators in Hilbert Spaces; Spectral Theorem for Self-adjoint Operators; Compact Operators and the Hilbert-Schmidt Theorem; Elements of Perturbation Theory; Variational Principles; One-Dimensional Schrödinger Operator; Multidimensional Schrödinger Operator; Periodic Schrödinger Operator; Quantum Graphs; Non-linear Schrödinger Equation; References; Index.



Semilinear Schrodinger Equations


Semilinear Schrodinger Equations
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Author : Thierry Cazenave
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Semilinear Schrodinger Equations written by Thierry Cazenave 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 2003 with Mathematics categories.


The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.



Regularity And Approximability Of Electronic Wave Functions


Regularity And Approximability Of Electronic Wave Functions
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Author : Harry Yserentant
language : en
Publisher: Springer
Release Date : 2010-05-19

Regularity And Approximability Of Electronic Wave Functions written by Harry Yserentant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-19 with Mathematics categories.


The electronic Schrodi ̈ nger equation describes the motion of N electrons under Coulomb interaction forces in a eld of clamped nuclei. Solutions of this equation depend on 3N variables, three spatial dimensions for each electron. Approxim- ing the solutions is thus inordinately challenging, and it is conventionally believed that a reduction to simpli ed models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to c- vince the reader that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The present notes arose from lectures that I gave in Berlin during the academic year 2008/09 to introduce beginning graduate students of mathematics into this subject. They are kept on an intermediate level that should be accessible to an audience of this kind as well as to physicists and theoretical chemists with a c- responding mathematical training.



Semi Classical Analysis For Nonlinear Schrodinger Equations Wkb Analysis Focal Points Coherent States Second Edition


Semi Classical Analysis For Nonlinear Schrodinger Equations Wkb Analysis Focal Points Coherent States Second Edition
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Author : Remi Carles
language : en
Publisher: World Scientific
Release Date : 2020-10-05

Semi Classical Analysis For Nonlinear Schrodinger Equations Wkb Analysis Focal Points Coherent States Second Edition written by Remi Carles and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-05 with Mathematics categories.


The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent.Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schrödinger equations in negative order Sobolev spaces.The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform.



The Nonlinear Schr Dinger Equation


The Nonlinear Schr Dinger Equation
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Author : Catherine Sulem
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-30

The Nonlinear Schr Dinger Equation written by Catherine Sulem 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 2007-06-30 with Mathematics categories.


Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.



Lectures On The Energy Critical Nonlinear Wave Equation


Lectures On The Energy Critical Nonlinear Wave Equation
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Author : Carlos E. Kenig
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-14

Lectures On The Energy Critical Nonlinear Wave Equation written by Carlos E. Kenig 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 2015-04-14 with Mathematics categories.


This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the "concentration-compactness/rigidity theorem method" introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the "global regularity and well-posedness" conjecture (defocusing case) and the "ground-state" conjecture (focusing case) in critical dispersive problems. The second part of the monograph describes the "channel of energy" method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the three-dimensional radial focusing energy critical wave equation. It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations. A co-publication of the AMS and CBMS.



The Schr Dinger Equation


The Schr Dinger Equation
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Author : F.A. Berezin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Schr Dinger Equation written by F.A. Berezin 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 Mathematics categories.


This volume deals with those topics of mathematical physics, associated with the study of the Schrödinger equation, which are considered to be the most important. Chapter 1 presents the basic concepts of quantum mechanics. Chapter 2 provides an introduction to the spectral theory of the one-dimensional Schrödinger equation. Chapter 3 opens with a discussion of the spectral theory of the multi-dimensional Schrödinger equation, which is a far more complex case and requires careful consideration of aspects which are trivial in the one-dimensional case. Chapter 4 presents the scattering theory for the multi-dimensional non-relativistic Schrödinger equation, and the final chapter is devoted to quantization and Feynman path integrals. These five main chapters are followed by three supplements, which present material drawn on in the various chapters. The first two supplements deal with general questions concerning the spectral theory of operators in Hilbert space, and necessary information relating to Sobolev spaces and elliptic equations. Supplement 3, which essentially stands alone, introduces the concept of the supermanifold which leads to a more natural treatment of quantization. Although written primarily for mathematicians who wish to gain a better awareness of the physical aspects of quantum mechanics and related topics, it will also be useful for mathematical physicists who wish to become better acquainted with the mathematical formalism of quantum mechanics. Much of the material included here has been based on lectures given by the authors at Moscow State University, and this volume can also be recommended as a supplementary graduate level introduction to the spectral theory of differential operators with both discrete and continuous spectra. This English edition is a revised, expanded version of the original Soviet publication.



Notes On Quantum Mechanics


Notes On Quantum Mechanics
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Author : Enrico Fermi
language : en
Publisher: University of Chicago Press
Release Date : 1995-07

Notes On Quantum Mechanics written by Enrico Fermi and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07 with Science categories.


The lecture notes presented here in facsimile were prepared by Enrico Fermi for students taking his course at the University of Chicago in 1954. They are vivid examples of his unique ability to lecture simply and clearly on the most essential aspects of quantum mechanics. At the close of each lecture, Fermi created a single problem for his students. These challenging exercises were not included in Fermi's notes but were preserved in the notes of his students. This second edition includes a set of these assigned problems as compiled by one of his former students, Robert A. Schluter. Enrico Fermi was awarded the Nobel Prize for Physics in 1938.



Qualitative Properties Of Dispersive Pdes


Qualitative Properties Of Dispersive Pdes
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Author : Vladimir Georgiev
language : en
Publisher: Springer Nature
Release Date : 2022-12-02

Qualitative Properties Of Dispersive Pdes written by Vladimir Georgiev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-02 with Mathematics categories.


This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.