Download Full eBooks in PDF
The Schrödinger Equation Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of The Schrödinger Equation book. This book definitely worth reading, it is an incredibly well-written.
Author : Daniel A. Fleisch
Publisher : Cambridge University Press
Page : 237 pages
File Size : 51,7 Mb
Release : 2020-02-20
Category : Mathematics
ISBN : 9781108834735
A clear guide to the key concepts and mathematical techniques underlying the Schrödinger equation, including homework problems and fully worked solutions.
Author : F.A. Berezin,M. Shubin
Publisher : Springer Science & Business Media
Page : 573 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401131544
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.
Author : Paul L. A. Popelier
Publisher : World Scientific
Page : 375 pages
File Size : 55,8 Mb
Release : 2011
Category : Science
ISBN : 9781848167254
The Schrodinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrodinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?
Author : Gadi Fibich
Publisher : Springer
Page : 862 pages
File Size : 41,8 Mb
Release : 2015-03-06
Category : Mathematics
ISBN : 9783319127484
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France
Author : M. Nagasawa
Publisher : Birkhäuser
Page : 335 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885683
Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.
Author : Thierry Cazenave
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 55,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821833995
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 : Catherine Sulem,Pierre-Louis Sulem
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 45,9 Mb
Release : 2007-06-30
Category : Mathematics
ISBN : 9780387227689
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.
Author : Walter Thirring,Paul Urban
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783709176733
On the occasion of the 50th anniversary of the discovery of the Schrodinger equation a small symposium was organized in Vienna. It had mainly retrospective character, where after an appreciation of Schrodinger's scientific achievements the results were collected which one could extract from his equation. Of course not all the developments which originated in Schrodingers dis coveries could be included. Instead, it was attempted to present a review of the established predictions which follow directly from his equation. Despite the 50 years of its existence there are always new results of this sort being found, especially because the necessary mathe matical methods are being developed and become known to the physicists slowly only now .. I want to take the opportunity here to thank the lecturers for their efforts which they put into their excellent talks and their written versions. With their help this volume should become a useful document on the current mathematical art in the treatment of the Schrodinger equation. Finally it is my pleasant obligation to thank the Bundesministerium fUr Wissenschaft und Forschung and the Kulturamt der Gemeinde Wien for their financial support which made it possible to honor one of the great Austrian scientists.
Author : Panayotis G. Kevrekidis
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 41,5 Mb
Release : 2009-07-07
Category : Science
ISBN : 9783540891994
This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.
Author : OpenStax
Publisher : Unknown
Page : 622 pages
File Size : 44,8 Mb
Release : 2016-11-04
Category : Science
ISBN : 1680920456
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. The text and images in this textbook are grayscale.
Author : Kai L. Chung,Zhongxin Zhao
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 42,9 Mb
Release : 2001-07-31
Category : Mathematics
ISBN : 3540570306
In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics. A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature.
Author : Harald Grosse,Andri Martin
Publisher : Cambridge University Press
Page : 183 pages
File Size : 48,9 Mb
Release : 1997-11-20
Category : Mathematics
ISBN : 9780521392259
Introduces theory and applications of the bound state problem in Schrödinger theory in particle physics.
Author : Tuncay Aktosun,Ricardo Weder
Publisher : Springer Nature
Page : 631 pages
File Size : 47,8 Mb
Release : 2020-05-19
Category : Mathematics
ISBN : 9783030384319
Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
Author : Serafin Fraga,José Manuel García de la Vega,Eric S. Fraga
Publisher : Springer
Page : 248 pages
File Size : 49,6 Mb
Release : 1999
Category : Computers
ISBN : UOM:39015057383302
The linear Schrödinger equation is central to Quantum Chemistry. It is presented within the context of relativistic Quantum Mechanics and analysed both in time-dependent and time-independent forms. The Riccati equation is used to study the one-dimensional Schrödinger equation. The authors develop the Schrödinger-Riccati equation as an approach to determine solutions of the time-independent, linear Schrödinger equation.
Author : Erwin Schrödinger
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 44,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821835241
The famous equation that bears Erwin Schrödinger's name encapsulates his profound contributions to quantum mechanics using wave mechanics. This third, augmented edition of his papers on the topic contains the six original, famous papers in which Schrödinger created and developed the subject of wave mechanics as published in the original edition. As the author points out, at the time each paper was written the results of the later papers were largely unknown to him. This edition also contains three papers that were written shortly after the original edition was published and four lectures delivered by Schrödinger at the Royal Institution in London in 1928. The papers and lectures in this volume were revised by the author and translated into English, and afford the reader a striking and valuable insight into how wave mechanics developed.
