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| quantum mechanics in hilbert space prugovecki: Quantum Mechanics in Hilbert Space Eduard Prugovečki, 1971 |
| quantum mechanics in hilbert space prugovecki: Quantum Mechanics in Hilbert Space Eduard Prugovecki, 2013-07-02 A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas. This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the gap between strictly physics- and mathematics-oriented texts on Hilbert space theory as applied to nonrelativistic quantum mechanics. Organized in the form of definitions, theorems, and proofs of theorems, it allows readers to immediately grasp the basic concepts and results. Exercises appear throughout the text, with hints and solutions at the end. |
| quantum mechanics in hilbert space prugovecki: Quantum Mechanics in Hilbert Space , 1982-08-18 Quantum Mechanics in Hilbert Space |
| quantum mechanics in hilbert space prugovecki: Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics W.-H. Steeb, 2013-03-07 This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics. |
| quantum mechanics in hilbert space prugovecki: Quantum Mechanics in Hilbert Space Eduard Prugověcki, 1984 |
| quantum mechanics in hilbert space prugovecki: Hilbert Space Methods in Quantum Mechanics Werner O. Amrein, 2009 |
| quantum mechanics in hilbert space prugovecki: Applied Analysis by the Hilbert Space Method Samuel S. Holland, 2007-06-05 Numerous worked examples and exercises highlight this unified treatment of the Hermitian operator theory in its Hilbert space setting. Its simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. Featuring full discussions of first and second order linear differential equations, the text introduces the fundamentals of Hilbert space theory and Hermitian differential operators. It derives the eigenvalues and eigenfunctions of classical Hermitian differential operators, develops the general theory of orthogonal bases in Hilbert space, and offers a comprehensive account of Schrödinger's equations. In addition, it surveys the Fourier transform as a unitary operator and demonstrates the use of various differentiation and integration techniques. Samuel S. Holland, Jr. is a professor of mathematics at the University of Massachusetts, Amherst. He has kept this text accessible to undergraduates by omitting proofs of some theorems but maintaining the core ideas of crucially important results. Intuitively appealing to students in applied mathematics, physics, and engineering, this volume is also a fine reference for applied mathematicians, physicists, and theoretical engineers. |
| quantum mechanics in hilbert space prugovecki: Quantum Theory for Mathematicians Brian C. Hall, 2013-06-19 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. |
| quantum mechanics in hilbert space prugovecki: Introduction to Hilbert Spaces with Applications Lokenath Debnath, Piotr Mikusinski, 2005-09-29 Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. - Updated chapter on wavelets - Improved presentation on results and proof - Revised examples and updated applications - Completely updated list of references |
| quantum mechanics in hilbert space prugovecki: Quantum Geometry Margaret Prugovecki, 1992-02-29 This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief. |
| quantum mechanics in hilbert space prugovecki: Quantum Logic in Algebraic Approach Miklós Rédei, 2013-03-09 This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J. |
| quantum mechanics in hilbert space prugovecki: Classical Systems in Quantum Mechanics Pavel Bóna, 2020-06-23 This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of microsystems and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement describing dynamical transitions from microsystems to macrosystems. |
| quantum mechanics in hilbert space prugovecki: Principles Of Quantum General Relativity Eduard Prugovecki, 1995-01-20 This monograph explains and analyzes the principles of a quantum-geometric framework for the unification of general relativity and quantum theory. By taking advantage of recent advances in areas like fibre and superfibre bundle theory, Krein spaces, gauge fields and groups, coherent states, etc., these principles can be consistently incorporated into a framework that can justifiably be said to provide the foundations for a quantum extrapolation of general relativity. This volume aims to present this approach in a way which places as much emphasis on fundamental physical ideas as on their precise mathematical implementation. References are also made to the ideas of Einstein, Bohr, Born, Dirac, Heisenberg and others, in order to set the work presented here in an appropriate historical context. |
| quantum mechanics in hilbert space prugovecki: Functional Analysis in Mechanics Leonid P. Lebedev, I. I. Vorovich, 2002-11-20 This is a self-contained book that covers the foundations of functional analysis while introducing the essential topics of the chosen applications. Graduate level students in mathematics and engineering will find the text useful. |
| quantum mechanics in hilbert space prugovecki: Foundations of Quantum Mechanics Josef Maria Jauch, 1977 |
| quantum mechanics in hilbert space prugovecki: Stochastic Quantum Mechanics and Quantum Spacetime Margaret Prugovecki, 2012-12-06 The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents. |
| quantum mechanics in hilbert space prugovecki: Challenges to The Second Law of Thermodynamics Vladislav Capek, Daniel P. Sheehan, 2006-03-30 The advance of scienti?c thought in ways resembles biological and geologic transformation: long periods of gradual change punctuated by episodes of radical upheaval. Twentieth century physics witnessed at least three major shifts — relativity, quantum mechanics and chaos theory — as well many lesser ones. Now, st early in the 21 , another shift appears imminent, this one involving the second law of thermodynamics. Over the last 20 years the absolute status of the second law has come under increased scrutiny, more than during any other period its 180-year history. Since the early 1980’s, roughly 50 papers representing over 20 challenges have appeared in the refereed scienti?c literature. In July 2002, the ?rst conference on its status was convened at the University of San Diego, attended by 120 researchers from 25 countries (QLSL2002) [1]. In 2003, the second edition of Le?’s and Rex’s classic anthology on Maxwell demons appeared [2], further raising interest in this emerging ?eld. In 2004, the mainstream scienti?c journal Entropy published a special edition devoted to second law challenges [3]. And, in July 2004, an echo of QLSL2002 was held in Prague, Czech Republic [4]. Modern second law challenges began in the early 1980’s with the theoretical proposals of Gordon and Denur. Starting in the mid-1990’s, several proposals for experimentally testable challenges were advanced by Sheehan, et al. By the late 1990’s and early 2000’s, a rapid succession of theoretical quantum mechanical ? challenges were being advanced by C ́ apek, et al. |
| quantum mechanics in hilbert space prugovecki: Lagrangian And Hamiltonian Mechanics: Solutions To The Exercises Melvin G Calkin, 1999-03-12 This book contains the exercises from the classical mechanics text Lagrangian and Hamiltonian Mechanics, together with their complete solutions. It is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course, but it may also be used, together with that text, by those who are studying mechanics on their own. |
| quantum mechanics in hilbert space prugovecki: Quantum Geometry Margaret Prugovecki, 2013-03-14 This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief. |
| quantum mechanics in hilbert space prugovecki: Mathematical Methods in Quantum Mechanics Gerald Teschl, 2009 |
| quantum mechanics in hilbert space prugovecki: Mathematics Without Numbers Geoffrey Hellman, 1989 Geoffrey Hellman presents a detailed interpretation of mathematics as the investigation of structural possibilities, as opposed to absolute, Platonic objects. After dealing with the natural numbers and analysis, he extends his approach to set theory, and shows how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world. |
| quantum mechanics in hilbert space prugovecki: Mathematical Foundations of Quantum Theory A.R. Marlow, 2012-12-02 Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory. |
| quantum mechanics in hilbert space prugovecki: Problem Solving Through Recreational Mathematics Bonnie Averbach, Orin Chein, 2012-03-15 Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. Free solutions manual available for download at the Dover website. |
| quantum mechanics in hilbert space prugovecki: Quantum Theory for Math Enthusiasts Sanjay Nair, 2025-02-20 Quantum Theory for Math Enthusiasts is tailored for undergraduate students with a strong mathematical background who wish to explore the profound connections between mathematics and quantum mechanics. We offer a comprehensive yet accessible introduction to the mathematical foundations of quantum mechanics. Starting with fundamental concepts from linear algebra, functional analysis, and probability theory, we gradually build the mathematical toolkit necessary to understand quantum theory. Through clear explanations, illustrative examples, and exercises, students will develop a solid understanding of Hilbert spaces, operators, eigenvalues, and other key mathematical structures underpinning quantum mechanics. We also explore advanced topics such as symmetry groups, Lie algebras, and representation theory, shedding light on the profound mathematical structures inherent in quantum theory. Whether you're a mathematics major interested in theoretical physics or a physics student looking to deepen your mathematical understanding, our book provides the foundation to appreciate the beauty and elegance of quantum theory from a mathematical perspective. |
| quantum mechanics in hilbert space prugovecki: Differential Geometry with Applications to Mechanics and Physics Yves Talpaert, 2000-09-12 An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises. |
| quantum mechanics in hilbert space prugovecki: Handbook of Quantum Logic and Quantum Structures Kurt Engesser, Dov M. Gabbay, Daniel Lehmann, 2011-08-11 Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled The logic of quantum mechanics quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.- Written by eminent scholars in the field of logic- A comprehensive presentation of the theory, approaches and results in the field of quantum logic- Volume focuses on quantum structures |
| quantum mechanics in hilbert space prugovecki: Modular Functions and Dirichlet Series in Number Theory Tom M. Apostol, 2012-12-06 This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. The second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj(r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject which in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T.M.A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory. |
| quantum mechanics in hilbert space prugovecki: Quantum Mechanics Using Computer Algebra Willi-hans Steeb, 1994-05-23 Solving problems in quantum mechanics is an essential skill and research activity for scientists, engineers and others. Nowadays the labor of scientific computation has been greatly eased by the advent of computer algebra packages. These do not merely perform number-crunching tasks, but enable users to manipulate algebraic expressions and equations symbolically. For example, differentiation and integration can now be carried out algebraically by the computer.This book collects standard and advanced methods in quantum mechanics and implements them using REDUCE, a popular computer algebra package. Throughout, sample programs and their output have been displayed alongside explanatory text, making the book easy to follow. Selected problems have also been implemented using two other popular packages, MATHEMATICA and MAPLE, and in the object-oriented programming language C++.Besides standard quantum mechanical techniques, modern developments in quantum theory are also covered. These include Fermi and Bose Operators, coherent states, gauge theory and quantum groups. All the special functions relevant to quantum mechanics (Hermite, Chebyshev, Legendre and more) are implemented.The level of presentation is such that one can get a sound grasp of computational techniques early on in one's scientific education. A careful balance is struck between practical computation and the underlying mathematical concepts, making the book well-suited for use with quantum mechanics courses. |
| quantum mechanics in hilbert space prugovecki: Symplectic Techniques in Physics Victor Guillemin, Shlomo Sternberg, 1990-05-25 Symplectic geometry is very useful for clearly and concisely formulating problems in classical physics and also for understanding the link between classical problems and their quantum counterparts. It is thus a subject of interest to both mathematicians and physicists, though they have approached the subject from different view points. This is the first book that attempts to reconcile these approaches. The authors use the uncluttered, coordinate-free approach to symplectic geometry and classical mechanics that has been developed by mathematicians over the course of the last thirty years, but at the same time apply the apparatus to a great number of concrete problems. In the first chapter, the authors provide an elementary introduction to symplectic geometry and explain the key concepts and results in a way accessible to physicists and mathematicians. The remainder of the book is devoted to the detailed analysis and study of the ideas discussed in Chapter 1. Some of the themes emphasized in the book include the pivotal role of completely integrable systems, the importance of symmetries, analogies between classical dynamics and optics, the importance of symplectic tools in classical variational theory, symplectic features of classical field theories, and the principle of general covariance. This work can be used as a textbook for graduate courses, but the depth of coverage and the wealth of information and application means that it will be of continuing interest to, and of lasting significance for mathematicians and mathematically minded physicists. |
| quantum mechanics in hilbert space prugovecki: Quantum Mechanics in Phase Space Cosmas Zachos, David Fairlie, Thomas Curtright, 2005 Wigner's quasi-probability distribution function in phase space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence, quantum computing, and quantum chaos. It is also important in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative, formulation of quantum mechanics, independent of the conventional Hilbert space, or path integral formulations.In this logically complete and self-standing formulation, one need not choose sides ? coordinate or momentum space. It works in full phase space, accommodating the uncertainty principle, and it offers unique insights into the classical limit of quantum theory. This invaluable book is a collection of the seminal papers on the formulation, with an introductory overview which provides a trail map for those papers; an extensive bibliography; and simple illustrations, suitable for applications to a broad range of physics problems. It can provide supplementary material for a beginning graduate course in quantum mechanics. |
| quantum mechanics in hilbert space prugovecki: The Emerging Quantum Luis de la Peña, Ana María Cetto, Andrea Valdés Hernández, 2014-07-15 This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics. The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physical mechanisms. The genesis of some of the central features of quantum theory is elucidated, such as atomic stability, the spin of the electron, quantum fluctuations, quantum nonlocality and entanglement. The theory developed here reaffirms fundamental scientific principles such as realism, causality, locality and objectivity. |
| quantum mechanics in hilbert space prugovecki: Lectures On Quantum Theory Mathematical And Structural Foundations Chris J. Isham, 2001 |
| quantum mechanics in hilbert space prugovecki: Smooth Dynamical Systems , 1980-08-12 Smooth Dynamical Systems |
| quantum mechanics in hilbert space prugovecki: Introduction to Global Analysis , 1980-09-19 Introduction to Global Analysis |
| quantum mechanics in hilbert space prugovecki: Physical Reality and Mathematical Description C.P. Enz, J. Mehra, 2012-12-06 This collection of essays is intended as a tribute to Josef Maria Jauch on his sixtieth birthd~. Through his scientific work Jauch has justly earned an honored name in the community of theo retical physicists. Through his teaching and a long line of dis tinguished collaborators he has put an imprint on modern mathema tical physics. A number of Jauch's scientific collaborators, friends and admirers have contributed to this collection, and these essays reflect to some extent Jauch's own wide interests in the vast do main of theoretical physics. Josef Maria Jauch was born on 20 September 1914, the son of Josef Alois and Emma (nee Conti) Jauch, in Lucerne, Switzerland. Love of science was aroused in him early in his youth. At the age of twelve he came upon a popular book on astronomy, and an exam ple treated in this book mystified him. It was stated that if a planet travels around a centre of Newtonian attraction with a pe riod T, and if that planet were stopped and left to fall into the centre from any point of the circular orbit, it would arrive at the centre in the time T/I32. Young Josef puzzled about this for several months until he made his first scientific discovery : that this result could be derived from Kepler's third law in a quite elementary way. |
| quantum mechanics in hilbert space prugovecki: The Mathematical Theory of L Systems , 1980-04-29 The Mathematical Theory of L Systems |
| quantum mechanics in hilbert space prugovecki: Kinematical Theory of Spinning Particles M. Rivas, 2006-04-11 Classical spin is described in terms of velocities and acceleration so that knowledge of advanced mathematics is not required. Written in the three-dimensional notation of vector calculus, it can be followed by undergraduate physics students, although some notions of Lagrangian dynamics and group theory are required. It is intended as a general course at a postgraduate level for all-purpose physicists. This book presents a unified approach to classical and quantum mechanics of spinning particles, with symmetry principles as the starting point. A classical concept of an elementary particle is presented. The variational statements to deal with spinning particles are revisited. It is shown that, by explicitly constructing different models, symmetry principles are sufficient for the description of either classical or quantum-mechanical elementary particles. Several spin effects are analyzed. |
| quantum mechanics in hilbert space prugovecki: Optimal Feedback for Stochastic Linear Quadratic Control and Backward Stochastic Riccati Equations in Infinite Dimensions Qi Lü, Xu Zhang, 2024-03-18 View the abstract. |
| quantum mechanics in hilbert space prugovecki: Viscoelasticity of Polymers Kwang Soo Cho, 2016-05-30 This book offers a comprehensive introduction to polymer rheology with a focus on the viscoelastic characterization of polymeric materials. It contains various numerical algorithms for the processing of viscoelastic data, from basic principles to advanced examples which are hard to find in the existing literature. The book takes a multidisciplinary approach to the study of the viscoelasticity of polymers, and is self-contained, including the essential mathematics, continuum mechanics, polymer science and statistical mechanics needed to understand the theories of polymer viscoelasticity. It covers recent achievements in polymer rheology, such as theoretical and experimental aspects of large amplitude oscillatory shear (LAOS), and numerical methods for linear viscoelasticity, as well as new insights into the interpretation of experimental data. Although the book is balanced between the theoretical and experimental aspects of polymer rheology, the author’s particular interest in the theoretical side will not remain hidden. Aimed at readers familiar with the mathematics and physics of engineering at an undergraduate level, the multidisciplinary approach employed enables researchers with various scientific backgrounds to expand their knowledge of polymer rheology in a systematic way. |
| quantum mechanics in hilbert space prugovecki: Hypervirial Theorems Francisco M. Fernandez, Eduardo Alberto Castro, 2012-12-06 |
Quantum - Wikipedia
In physics, a quantum (pl.: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" …
Quantum | Definition & Facts | Britannica
May 31, 2025 · Quantum, in physics, discrete natural unit, or packet, of energy, charge, angular momentum, or other physical property. Light, for example, appearing in some respects as a …
What Is Quantum Physics? - Caltech Science Exchange
Quantum physics is the study of matter and energy at the most fundamental level. It aims to uncover the properties and behaviors of the very building blocks of nature. While many …
Demystifying Quantum: It’s Here, There and Everywhere
Apr 10, 2024 · Quantum, often called quantum mechanics, deals with the granular and fuzzy nature of the universe and the physical behavior of its smallest particles. The idea of physical …
Quantum mechanics: Definitions, axioms, and key concepts of quantum …
Apr 29, 2024 · Quantum mechanics, or quantum physics, is the body of scientific laws that describe the wacky behavior of photons, electrons and the other subatomic particles that make …
What is quantum in physics and computing? - TechTarget
Feb 27, 2025 · A quantum, the singular form of quanta, is the smallest discrete unit of any physical entity. For example, a quantum of light is a photon, and a quantum of electricity is an …
Science 101: Quantum Mechanics - Argonne National Laboratory
So, what is quantum? In a more general sense, the word “ quantum” can refer to the smallest possible amount of something. The field of quantum mechanics deals with the most …
DOE Explains...Quantum Mechanics | Department of Energy
Quantum mechanics is the field of physics that explains how extremely small objects simultaneously have the characteristics of both particles (tiny pieces of matter) and waves (a …
Quantum for dummies: the basics explained | Engineering and …
Apr 16, 2019 · Professor Alan Woodward from the University of Surrey attempts to demystify the quantum world by explaining key terminology and theory. Which atoms and particles does …
Quantum - definition of quantum by The Free Dictionary
A unit of energy, especially electromagnetic energy, that is the smallest physical quantity that can exist on its own. A quantum acts both like a particle and like an energy wave. Photons are …
Quantum - Wikipedia
In physics, a quantum (pl.: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" …
Quantum | Definition & Facts | Britannica
May 31, 2025 · Quantum, in physics, discrete natural unit, or packet, of energy, charge, angular momentum, or other physical property. Light, for example, appearing in some respects as a …
What Is Quantum Physics? - Caltech Science Exchange
Quantum physics is the study of matter and energy at the most fundamental level. It aims to uncover the properties and behaviors of the very building blocks of nature. While many …
Demystifying Quantum: It’s Here, There and Everywhere
Apr 10, 2024 · Quantum, often called quantum mechanics, deals with the granular and fuzzy nature of the universe and the physical behavior of its smallest particles. The idea of physical …
Quantum mechanics: Definitions, axioms, and key concepts of quantum …
Apr 29, 2024 · Quantum mechanics, or quantum physics, is the body of scientific laws that describe the wacky behavior of photons, electrons and the other subatomic particles that make …
What is quantum in physics and computing? - TechTarget
Feb 27, 2025 · A quantum, the singular form of quanta, is the smallest discrete unit of any physical entity. For example, a quantum of light is a photon, and a quantum of electricity is an …
Science 101: Quantum Mechanics - Argonne National Laboratory
So, what is quantum? In a more general sense, the word “ quantum” can refer to the smallest possible amount of something. The field of quantum mechanics deals with the most …
DOE Explains...Quantum Mechanics | Department of Energy
Quantum mechanics is the field of physics that explains how extremely small objects simultaneously have the characteristics of both particles (tiny pieces of matter) and waves (a …
Quantum for dummies: the basics explained | Engineering and …
Apr 16, 2019 · Professor Alan Woodward from the University of Surrey attempts to demystify the quantum world by explaining key terminology and theory. Which atoms and particles does …
Quantum - definition of quantum by The Free Dictionary
A unit of energy, especially electromagnetic energy, that is the smallest physical quantity that can exist on its own. A quantum acts both like a particle and like an energy wave. Photons are …
