Lecture Notes on Schrödinger Equations PDF Download
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Author: Aleksandr Andreevich Pankov
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 208
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Book Description
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.
Author: Aleksandr Andreevich Pankov
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 208
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Book Description
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.
Author: Thierry Cazenave
Publisher: American Mathematical Soc.
ISBN: 0821833995
Category : Mathematics
Languages : en
Pages : 346
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Book Description
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.
Author: Steven Weinberg
Publisher: Cambridge University Press
ISBN: 131636903X
Category : Science
Languages : en
Pages : 443
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Book Description
Nobel Laureate Steven Weinberg combines exceptional physical insight with his gift for clear exposition, to provide a concise introduction to modern quantum mechanics, in this fully updated second edition of his successful textbook. Now including six brand new sections covering key topics such as the rigid rotator and quantum key distribution, as well as major additions to existing topics throughout, this revised edition is ideally suited to a one-year graduate course or as a reference for researchers. Beginning with a review of the history of quantum mechanics and an account of classic solutions of the Schrödinger equation, before quantum mechanics is developed in a modern Hilbert space approach, Weinberg uses his remarkable expertise to elucidate topics such as Bloch waves and band structure, the Wigner–Eckart theorem, magic numbers, isospin symmetry, and general scattering theory. Problems are included at the ends of chapters, with solutions available for instructors at www.cambridge.org/9781107111660.
Author: ?akir Erko
Publisher: World Scientific
ISBN: 9789810228118
Category : Science
Languages : en
Pages : 330
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Book Description
This book aims to present a unified account of the physics of atoms and molecules from a modern viewpoint. It is based on courses given by the authors at Middle East Technical University, Ankara and Georgia Institute of Technology, Atlanta, and is suitable for study at third and fourth year levels of an undergraduate course.Students should be able to read this volume and understand its contents without the need to supplement it by referring to more detailed discussions. The whole subject covered in this volume is expected to be finished in one semester.
Author: Samuel D. Lindenbaum
Publisher: World Scientific
ISBN: 9789810238391
Category : Science
Languages : en
Pages : 358
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Book Description
The chapters are not independent, but build on one another. Subjects range from the failures of classical theory to second quantization, including chapters on the Dirac theory and Feynman diagrams."--Pub. desc.
Author: Jens Hoppe
Publisher: Springer Science & Business Media
ISBN: 3540472746
Category : Science
Languages : en
Pages : 109
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Book Description
Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.
Author: Thierry Cazenave
Publisher:
ISBN: 9781470417604
Category :
Languages : en
Pages : 323
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Book Description
Author: Peter E. Zhidkov
Publisher: Springer Science & Business Media
ISBN: 3540418334
Category : Mathematics
Languages : en
Pages : 153
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Book Description
The emphasis of this book is on questions typical of nonlinear analysis and qualitative theory of PDEs. The selection of the material is related to the author's attempt to illuminate those particularly interesting questions not yet covered in other monographs though they have been the subject of published articles. One chapter, for example, is devoted to the construction of invariant measures for dynamical systems generated by certain equations and a result from a recent paper on basic properties of a system of eigenfunctions of a stationary problem. Also considered is an application of the method of qualitative theory of ODes to proving the existence of radial solutions of stationary problems and stability of solutions of NLSE nonvanishing as the spatial variable tends to infinity. Finally a recent result on the existence of an infinite sequence of invariant measures for the inegrable KdV equation is presented.
Author: Erik Balslev
Publisher: Springer
ISBN: 3540471197
Category : Science
Languages : en
Pages : 227
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Book Description
Author: Remi Carles
Publisher: World Scientific
ISBN: 9814471747
Category : Mathematics
Languages : en
Pages : 256
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Book Description
These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated.These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided.
