An Introduction To The Functional Formulation Of Quantum Mechanics
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An Introduction To The Functional Formulation Of Quantum Mechanics
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Author : Horacio Oscar Girotti
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013-08-07
An Introduction To The Functional Formulation Of Quantum Mechanics written by Horacio Oscar Girotti and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-07 with Science categories.
The functional formulation of quantum mechanics and relativistic quantum field theories are widely studied subjects. Nevertheless, certain aspects of this formulation are frequently overlooked, in spite of their relevance from a structural point of view. This book aims to fill up this gap. The non-relativistic regime has been found particularly appropriate for these purposes.
Quantum Theory For Mathematicians
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Author : Brian C. Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-19
Quantum Theory For Mathematicians written by Brian C. Hall 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 2013-06-19 with Science categories.
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.
Functional Methods In Quantum Field Theory And Statistical Physics
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Author : A.N. Vasiliev
language : en
Publisher: CRC Press
Release Date : 1998-07-28
Functional Methods In Quantum Field Theory And Statistical Physics written by A.N. Vasiliev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-28 with Science categories.
Providing a systematic introduction to the techniques which are fundamental to quantum field theory, this book pays special attention to the use of these techniques in a wide variety of areas, including ordinary quantum mechanics, quantum mechanics in the second-quantized formulation, relativistic quantum field theory, Euclidean field theory, quantum statistics at finite temperature, and the classical statistics of nonideal gas and spin systems. The extended chapter on variational methods and functional Legendre transformations contains completely original material.
An Introduction To The Mathematical Structure Of Quantum Mechanics
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Author : F. Strocchi
language : en
Publisher: World Scientific
Release Date : 2008
An Introduction To The Mathematical Structure Of Quantum Mechanics written by F. Strocchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.
An Introduction To Quantum Field Theory
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Author : Michael E. Peskin
language : en
Publisher: CRC Press
Release Date : 2018-05-04
An Introduction To Quantum Field Theory written by Michael E. Peskin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Science categories.
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.
Formulation And Numerical Solution Of Quantum Control Problems
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Author : Alfio Borzi
language : en
Publisher: SIAM
Release Date : 2017-07-06
Formulation And Numerical Solution Of Quantum Control Problems written by Alfio Borzi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Mathematics categories.
This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods. ??
The Formalisms Of Quantum Mechanics
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Author : Francois David
language : en
Publisher: Springer
Release Date : 2014-11-06
The Formalisms Of Quantum Mechanics written by Francois David and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-06 with Science categories.
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and special relativity through their common roots - causality, locality and reversibility, as well as on the relation between quantum theory, information theory, correlations and measurements, and quantum gravity. Quantum mechanics is probably the most successful physical theory ever proposed and despite huge experimental and technical progresses in over almost a century, it has never been seriously challenged by experiments. In addition, quantum information science ha s become an important and very active field in recent decades, further enriching the many facets of quantum physics. Yet, there is a strong revival of the discussions about the principles of quantum mechanics and its seemingly paradoxical aspects: sometimes the theory is portrayed as the unchallenged and dominant paradigm of modern physical sciences and technologies while sometimes it is considered a still mysterious and poorly understood theory, waiting for a revolution. This volume, addressing graduate students and seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics.
Modern Quantum Field Theory
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Author : Tom Banks
language : en
Publisher: Cambridge University Press
Release Date : 2008-09-18
Modern Quantum Field Theory written by Tom Banks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-18 with Science categories.
Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets
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Author : Hagen Kleinert
language : en
Publisher: World Scientific
Release Date : 2009
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets written by Hagen Kleinert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Business & Economics categories.
Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.
Feynman Path Integrals In Quantum Mechanics And Statistical Physics
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Author : Lukong Cornelius Fai
language : en
Publisher: CRC Press
Release Date : 2021-04-15
Feynman Path Integrals In Quantum Mechanics And Statistical Physics written by Lukong Cornelius Fai and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Science categories.
This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations. Features: Comprehensive and rigorous yet, presents an easy-to-understand approach. Applicable to a wide range of disciplines. Accessible to those with little, or basic, mathematical understanding.