Download or read book Probability and Schr dinger s Mechanics written by David B. Cook and published by World Scientific. This book was released on 2002 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses some of the problems of interpreting Schrdinger's mechanics ? the most complete and explicit theory falling under the umbrella of ?quantum theory?. The outlook is materialist (?realist?) and stresses the development of Schrdinger's mechanics from classical theories and its close connections with (particularly) the Hamilton?Jacobi theory. Emphasis is placed on the concepts and use of the modern objective (measure-theoretic) probability theory. The work is free from any mention of the bearing of Schrdinger's mechanics on God, his alleged mind or, indeed, minds at all. The author has taken the nave view that this mechanics is about the structure and dynamics of atomic and sub-atomic systems since he has been unable to trace any references to minds, consciousness or measurements in the foundations of the theory.
Download or read book Probability and Schr dinger s Mechanics written by David B Cook and published by World Scientific. This book was released on 2002-12-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses some of the problems of interpreting Schrödinger's mechanics — the most complete and explicit theory falling under the umbrella of “quantum theory”. The outlook is materialist (“realist”) and stresses the development of Schrödinger's mechanics from classical theories and its close connections with (particularly) the Hamilton–Jacobi theory. Emphasis is placed on the concepts and use of the modern objective (measure-theoretic) probability theory. The work is free from any mention of the bearing of Schrödinger's mechanics on God, his alleged mind or, indeed, minds at all. The author has taken the naïve view that this mechanics is about the structure and dynamics of atomic and sub-atomic systems since he has been unable to trace any references to minds, consciousness or measurements in the foundations of the theory. Contents:Preliminaries:Orientation and OutlookProbabilities:Simple ProbabilitiesA More Careful Look at ProbabilitiesClassical Mechanics:The Hamilton–Jacobi EquationAngular MomentumSchrödinger's Mechanics:Prelude: Particle DiffractionThe Genesis of Schrödinger's MechanicsThe Schrödinger EquationIdentities: Momenta and Dynamical VariablesAbstracting the StructureInterpretation from Applications:The Quantum Kepler ProblemThe Harmonic Oscillator and FieldsPerturbation Theory and EpicyclesFormalisms and “Hidden” VariablesDisputes and Paradoxes:Measurement at the Microscopic LevelParadoxesBeyond Schrödinger's Mechanics? Readership: Physical scientists interested in quantum theory, philosophers of science, and students of scientific philosophy. Keywords:Physical Science;Quantum Theory;Probability Theory;Philosophy of Science;Schrödinger's Mechanics;Classical MechanicsReviews:“The book can be recommended to students who do not feel satisfied by the inductive part of their textbooks as well as to people who just want to know how to understand quantum mechanics on a moderate level.”Zentralblatt MATH
Download or read book Schr dinger Diffusion Processes written by Robert Aebi and published by Springer Science & Business Media. This book was released on 1996-02-29 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931 Erwin Schrödinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times. What is the "most probable" state of the cloud at intermediate times? The present book provides a general yet comprehensive discourse on Schrödinger's question. Key roles in this investigation are played by conditional diffusion processes, pairs of non-linear integral equations and interacting particles systems. The introductory first chapter gives some historical background, presents the main ideas in a rather simple discrete setting and reveals the meaning of intermediate prediction to quantum mechanics. In order to answer Schrödinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations. The book presumes a graduate level of knowledge in mathematics or physics and represents a relevant and demanding application of today's advanced probability theory.
Download or read book Schr dinger Equations and Diffusion Theory written by Masao Nagasawa and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 tells 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. --- This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the profound mathematical properties of diffusion processes. (Mathematical Reviews)
Download or read book Schrodinger s Mechanics Interpretation written by Cook David B and published by World Scientific. This book was released on 2018-04-05 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interpretation of quantum mechanics has been in dispute for nearly a century with no sign of a resolution. Using a careful examination of the relationship between the final form of classical particle mechanics (the Hamilton-Jacobi Equation) and Schrödinger's mechanics, this book presents a coherent way of addressing the problems and paradoxes that emerge through conventional interpretations. Schrödinger's Mechanics critiques the popular way of giving physical interpretation to the various terms in perturbation theory and other technologies and places an emphasis on development of the theory and not on an axiomatic approach. When this interpretation is made, the extension of Schrödinger's mechanics in relation to other areas, including spin, relativity and fields, is investigated and new conclusions are reached. Contents: AimsBasics: The Schrödinger ConditionThe Dimensions of SpaceMomenta, Operators, and a ProblemApproximation and InterpretationSpin in Schrödinger's TheoryRelativistic EquationsFields and Second Quantisation Readership: Physicists, chemists, philosophers of science, anyone with an interest in physical science. Keywords: Quantum Theory;Interpretation;Wave Mechanics;Quantum PhilosophyReview: Key Features: Gives a unique interpretation of the topic
Download or read book Schr dinger s Philosophy of Quantum Mechanics written by Michael Bitbol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the final outcome of two projects. My first project was to publish a set of texts written by Schrodinger at the beginning of the 1950's for his seminars and lectures at the Dublin Institute for Advanced Studies. These almost completely forgotten texts contained important insights into the interpretation of quantum mechanics, and they provided several ideas which were missing or elusively expressed in SchrOdinger's published papers and books of the same period. However, they were likely to be misinterpreted out of their context. The problem was that current scholarship could not help very much the reader of these writings to figure out their significance. The few available studies about SchrOdinger's interpretation of quantum mechanics are generally excellent, but almost entirely restricted to the initial period 1925-1927. Very little work has been done on Schrodinger's late views on the theory he contributed to create and develop. The generally accepted view is that he never really recovered from his interpretative failure of 1926-1927, and that his late reflections (during the 1950's) are little more than an expression of his rising nostalgia for the lost ideal of picturing the world, not to say for some favourite traditional picture. But the content and style of Schrodinger's texts of the 1950's do not agree at all with this melancholic appraisal; they rather set the stage for a thorough renewal of accepted representations. In order to elucidate this paradox, I adopted several strategies.
Download or read book Introduction to Quantum Mechanics written by David J. Griffiths and published by Cambridge University Press. This book was released on 2019-11-20 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Changes and additions to the new edition of this classic textbook include a new chapter on symmetries, new problems and examples, improved explanations, more numerical problems to be worked on a computer, new applications to solid state physics, and consolidated treatment of time-dependent potentials.
Download or read book The Schr dinger Equation written by Walter Thirring and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Collected Papers on Wave Mechanics written by Erwin Schrödinger and published by American Mathematical Society. This book was released on 2001-10-04 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Frontiers in Analysis and Probability written by Nalini Anantharaman and published by Springer Nature. This book was released on 2020-11-21 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg–Zürich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zürich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum Yang–Mills theory, Gibbs measures of nonlinear Schrödinger equations, interfaces in spectral asymptotics and nodal sets. Contributions in this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.
Download or read book Solving the Schrodinger Equation written by Paul L. A. Popelier and published by World Scientific. This book was released on 2011 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?
Download or read book The Concept of Probability written by E.I. Bitsakis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles from invited speakers at a meeting which took place in Delphi, during the week of October 12-16, 1987. The theme of the meeting was ''The concept of probability" and was organized by the "Group of Interdisciplinary Research" (Physics Department, University of Athens) and the Theoretical and Physical Chemistry Institute of the National Hellenic Research Foundation, Athens. (The Group ofInterdisciplinary Research organized two previous Meetings, 1) on the Concept of physical reality (1982) and 2) on the question of determinism in Physics (1984». This small gathering, which was attended by scientists, mathematicians and philosophers from more than 22 countries, took place on the occasion of the 100th year from the birthday of E.Schrodinger. As the father of wave-mechanics, Schrodinger thrushed us into an era of physics where knowledge of the lV-function is considered, for most situations, as the ultimate aim and the ultimate truth. Yet, he, as well as another towering figure of 20th century physics, A.Einstein, never really felt confortable with the interpretation of the meaning oflV and of the information that it contains. With Einstein playing the leading role a debate about concepts and interpretation started as soon as quantum mechanics was born. Central theme to this debate is the concept of probability, a concept which permeates-explicitly or implicitly-all science and even our decision making in everyday life. The articles cover a broad spectrum of thought and results -mathematical, physical, epistemological, experimental, specific, general,-many of them outside the accepted norm.
Download or read book Epistemology and Probability written by Arkady Plotnitsky and published by Springer Science & Business Media. This book was released on 2009-10-20 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin Schro- ̈ dinger, and in quantum mechanics and in modern physics as a whole. It also considers the implications of these relationships and of quantum theory itself for our understanding of the nature of human thinking and knowledge in general, or the ‘‘epistemological lesson of quantum mechanics,’’ as Bohr liked 1 to say. These implications are radical and controversial. While they have been seen as scientifically productive and intellectually liberating to some, Bohr and Heisenberg among them, they have been troublesome to many others, such as Schro ̈ dinger and, most prominently, Albert Einstein. Einstein famously refused to believe that God would resort to playing dice or rather to playing with nature in the way quantum mechanics appeared to suggest, which is indeed quite different from playing dice. According to his later (sometime around 1953) remark, a lesser known or commented upon but arguably more important one: ‘‘That the Lord should play [dice], all right; but that He should gamble according to definite rules [i. e. , according to the rules of quantum mechanics, rather than 2 by merely throwing dice], that is beyond me. ’’ Although Einstein’s invocation of God is taken literally sometimes, he was not talking about God but about the way nature works. Bohr’s reply on an earlier occasion to Einstein’s question 1 Cf.
Download or read book The Meaning of the Wave Function written by Shan Gao and published by Cambridge University Press. This book was released on 2017-03-16 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function. Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain. A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics.
Download or read book Stochastic Processes in Quantum Physics written by Masao Nagasawa and published by Birkhäuser. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level. The book under review is recommended to mathematicians, physicists and graduate students interested in mathematical physics and stochastic processes. Furthermore, some selected chapters can be used as sub-textbooks for advanced courses on stochastic processes, quantum theory and quantum chemistry." ZAA
Download or read book Introduction to Quantum Mechanics written by Harald J W Müller-Kirsten and published by World Scientific Publishing Company. This book was released on 2012-07-19 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions. In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.
Download or read book Probability Mechanics written by Louis M. Houston and published by . This book was released on 2017-11-30 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability mechanics is a modified quantum mechanics, and it derives the modifications to physical quantities, including fields that determine whether these quantities are quantum mechanical or deterministic. Essentially, probability mechanics shows how information gets converted into energy through the propagation of probability waves through causal chains. Probability mechanics proves that the universe was not created by intelligence, and it proves that the gravitational field is deterministic and, therefore, not compatible with quantum mechanics.
