Connection Between Quantum And Classical Mechanics
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Connection Between Quantum And Classical Mechanics
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Author : Robert Francis McCann
language : en
Publisher:
Release Date : 1982
Connection Between Quantum And Classical Mechanics written by Robert Francis McCann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mechanics, Analytic categories.
Classical Mechanics And Quantum Mechanics An Historic Axiomatic Approach
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Author : Peter Enders
language : en
Publisher: Bentham Science Publishers
Release Date : 2019-09-05
Classical Mechanics And Quantum Mechanics An Historic Axiomatic Approach written by Peter Enders and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-05 with Science categories.
This unique textbook presents a novel, axiomatic pedagogical path from classical to quantum physics. Readers are introduced to the description of classical mechanics, which rests on Euler’s and Helmholtz’s rather than Newton’s or Hamilton’s representations. Special attention is given to the common attributes rather than to the differences between classical and quantum mechanics. Readers will also learn about Schrödinger’s forgotten demands on quantization, his equation, Einstein’s idea of ‘quantization as selection problem’. The Schrödinger equation is derived without any assumptions about the nature of quantum systems, such as interference and superposition, or the existence of a quantum of action, h. The use of the classical expressions for the potential and kinetic energies within quantum physics is justified. Key features: · Presents extensive reference to original texts. · Includes many details that do not enter contemporary representations of classical mechanics, although these details are essential for understanding quantum physics. · Contains a simple level of mathematics which is seldom higher than that of the common (Riemannian) integral. · Brings information about important scientists · Carefully introduces basic equations, notations and quantities in simple steps This book addresses the needs of physics students, teachers and historians with its simple easy to understand presentation and comprehensive approach to both classical and quantum mechanics..
Classical Dynamics And Its Quantum Analogues
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Author : David Park
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Dynamics And Its Quantum Analogues written by David Park 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 Science categories.
The short Heroic Age of physics that started in 1925 was one of the rare occasions when a deep consideration of the question: What does physics really say? was necessary in carrying out numerical calculations. In many parts of microphysics the calculations have now become relatively straightforward if not easy, but most physicists seem to agree that some questions of principle remain to be resolved, even if they do not think it is very important to do so. This situation has affected the way people think and write about quantum mechanics, a gingerly approach to fundamentals and a tendency to emphasize what fifty years ago was new in the new theory at the expense of continuity with what came before it. Nowadays those who look into the subject are more likely to be struck by unexpected similarities between quantum and classical mechanics than by dramatic contrasts they had been led to expect. It is often said that the hardest part of understanding quantum mechanics is to understand that there is nothing to understand; all the same, to think quantum mechanically it helps to have firm mental connections with classical physics and to know exactly what these connections do and do not imply. This book originated more than a decade ago as informal lecture notes [OP, prepared for use in a course taught from time to time to advanced undergraduates at Williams College.
Quantum Versus Classical Mechanics And Integrability Problems
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Author : Maciej Błaszak
language : en
Publisher: Springer
Release Date : 2019-06-11
Quantum Versus Classical Mechanics And Integrability Problems written by Maciej Błaszak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Science categories.
This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.
Theoretical And Quantum Mechanics
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Author : Stefan Ivanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-03
Theoretical And Quantum Mechanics written by Stefan Ivanov 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 2006-10-03 with Science categories.
This book has emerged from an undergraduate course as well as a graduate one, which I have taught for a number of years. Recently, many universities have experimented by bringing quantum theory forward in the curriculum and we follow their example. This book is intended to serve as an introduction to theoretical mechanics and quantum mechanics for chemists. I have included those parts of quantum mechanics which are of greatest fundamental interest and utility, and have developed those parts of classical mechanics which relate to and illuminate them. I try to give a comprehensive treatment wherever possible. The book would acquaint chemists with the quantum structure of the basic object of chemistry, the atom. My intention is to bridge the gap between classical physics, general and inorganic chemistry, and quantum mechanics. For these reasons: 1. I present in one course the basics of theoretical mechanics and quantum mechanics, to emphasise the continuity between them; 2. I have chosen the topics of theoretical mechanics based upon two criteria: a) usefulness for chemical problems: two-body problem; rotational motion of a charged particles (free and in an atom); interaction of a magnetic field with a magnetic dipole; details of small oscillations and oscillations of molecules; b) the need for transition from classical to quantum mechanics: basics of Lagrangian mechanics; basics of Hamiltonian mechanics; 3. I give detailed explanation of an application of the quantum method to simple systems: one-dimensional potential, harmonic oscillator, hydrogen atom, and hydrog- like atoms.
Unification Of Classical Quantum And Relativistic Mechanics And Of The Four Forces
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Author : J. X. Zheng-Johansson
language : en
Publisher: Nova Publishers
Release Date : 2006
Unification Of Classical Quantum And Relativistic Mechanics And Of The Four Forces written by J. X. Zheng-Johansson and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
In this book Drs J X Zheng-Johansson and Per-Ivar Johansson present a remarkable unification scheme. The scheme is based on an analysis of the overall experimental observations available up to today, and an observation of the unsolved problems maintained in contemporary theoretical physics, revisiting past controversies and putting them in context with contemporary physics. The unsolved problems were the agent stimulating the authors to invent a new bold unification scheme. Vacuum polarisation, with a vacuuon (a pair of strongly bound opposite-signed charges) as a free entity, gets you back to the days of the ether concept, abandoned by physics after the Michelson-Morley experiment by the end of the 19:th century. Starting from constructing the fundamental building blocks for the vacuum and material particles, the Newtonian-Maxwellian solutions the authors obtain yield insights into fundamental concepts such as vacuum, charge, and mass. For instance, can vacuum be described by a building block denoted vacuuon, with or without mass depending on pushed into motion or not? Can free charges be described as a mass-less entity? Can and how vacuum polarise? However, even if vacuum in the real Universe never polarises as proposed in this unification scheme, it may yet serve as another tool in the physics toolbox, a theoretical bridge between classical and modern physics. Physics and physical theory is a human invention, a mathematical description of the intrinsic properties of the Universe and its associated phenomena. Our understanding of the Universe is a reaction of our mind, of our way of understanding. Richard Feynman once noted about the Maxwell equations something that goes like: If a mathematical theory in physics cannot be proved by experiments it remains to be proved mathematically. Ultimately, it must be possible to test any new theory by experiments. If experimental tests are not possible we are left with a mere hypothesis based on equations. The unification scheme proposed by this work consists of a Proposition about the fundamental building blocks (ap- and n-vaculeon) and a series of Predictions from Newtonian-Maxwellian solutions based on that Proposition. The arriving at the Proposition and the Predictions, relating to classical, quantum and relativistic mechanics, is their context. The book is a challenge out of the ordinary, a challenge that deserves careful consideration.
Quantum Classical Analogies
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Author : Daniela Dragoman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Quantum Classical Analogies written by Daniela Dragoman 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 2013-04-09 with Science categories.
It is unanimously accepted that the quantum and the classical descriptions of the physical reality are very different, although any quantum process is "mysteriously" transformed through measurement into an observable classical event. Beyond the conceptual differences, quantum and classical physics have a lot in common. And, more important, there are classical and quantum phenomena that are similar although they occur in completely different contexts. For example, the Schrödinger equation has the same mathematical form as the Helmholtz equation, there is an uncertainty relation in optics very similar to that in quantum mechanics, and so on; the list of examples is very long. Quantum-classical analogies have been used in recent years to study many quantum laws or phenomena at the macroscopic scale, to design and simulate mesoscopic devices at the macroscopic scale, to implement quantum computer algorithms with classical means, etc. On the other hand, the new forms of light – localized light, frozen light – seem to have more in common with solid state physics than with classical optics. So these analogies are a valuable tool in the quest to understand quantum phenomena and in the search for new (quantum or classical) applications, especially in the area of quantum devices and computing.
Quantum Mechanics A Philosophical Perspective
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Author : Don Hainesworth
language : en
Publisher: AuthorHouse
Release Date : 2019-09-17
Quantum Mechanics A Philosophical Perspective written by Don Hainesworth and has been published by AuthorHouse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-17 with Science categories.
This book gives a comprehensive treatment on the historical discoveries and scientific developments concerning the Universe at the atomic and subatomic levels. Discussions begin with classical discoveries on the behavior of the atom to Quantum Mechanics and ends with exciting modern discoveries that are leading us to unlocking the hidden mysteries of reality. “Quantum mechanics describes the behavior of very small objects – the size of atoms or smaller – and it provides the only understanding of the world of the very small. In the world of quantum mechanics, the laws of physics that are familiar from the everyday world no longer work. Instead, events are governed by probabilities. During the time of Newton, it was thought that the Universe ran like clockwork, wound up and set in motion by the Creator, down some utterly predictable path. Newton’s classical mechanics provided plenty of support for this deterministic view of the Universe, a picture that left little place for human free will or chance. Could it really be that we are all puppets following our own preset tracks through life, with no real choice at all? Most scientists were content to let the philosophers debate that question. But it returned, with full force, at the heart of the new physics of the twentieth century.” In Search Of Schrodinger’s Cat – John Gribbin In addition, the various interpretations of quantum phenomena has led scientists and philosophers to a real possibility of finding a connection between matter and consciousness. This book contains no advanced scientific concepts, and no complicated formulas are written down for analysis. However, it does present some simple mathematical related examples in the final chapter. This is presented in order to reinforce the important ideas in QM and maintain a clear understanding of its fundamentals. It is not assumed that the reader has an understanding of Quantum Physics. Therefore the text provides the reader with enough historical and scientific information to insure his or her confidence in understanding the properties and behavior of quantum particle/wave elements.
Quantum Classical Correspondence
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Author : A. O. Bolivar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Quantum Classical Correspondence written by A. O. Bolivar 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 2013-04-09 with Science categories.
At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.
Quantum Mechanics
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Author : A. S. Davydov
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Quantum Mechanics written by A. S. Davydov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
Quantum Mechanics, Second Edition discusses the fundamental concepts and governing principles of quantum mechanics. The title details the physical ideas and the mathematical formalism of the quantum theory of the non-relativistic and quasi-relativistic motion of a single particle in an external field. The text first covers the basic concepts, and then proceeds to tackling the change of quantum states in time. Next, the selection examines the connection between quantum mechanics and classical mechanics. The book also discusses the simplest applications of quantum mechanics, along with the elementary representation theory. The book will be most useful to students of physics who are studying quantum mechanics. The text will also serve expert quantum physicists as a reference.