Introduction To Quantum Mechanics Schr Dinger Equation And Path Integral
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Introduction To Quantum Mechanics
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Author : Harald J W Müller-Kirsten
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-07-19
Introduction To Quantum Mechanics written by Harald J W Müller-Kirsten 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 2012-07-19 with Science categories.
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.
Introduction To Quantum Mechanics
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Author : H. J. W. Mller-Kirsten
language : en
Publisher: World Scientific
Release Date : 2006
Introduction To Quantum Mechanics written by H. J. W. Mller-Kirsten and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schrdinger equation on the one hand and the applications of the path integral on the other. Different from traditional texts and using a systematic perturbation method, the solution of Schrdinger equations includes also those with anharmonic oscillator potentials, periodic potentials, screened Coulomb potentials and a typical singular potential, as well as the investigation of the large order behavior of the perturbation series. On the path integral side, after introduction of the basic ideas, the expansion around classical configurations in Euclidean time, such as instantons, is considered, and the method is applied in particular to anharmonic oscillator and periodic potentials. Numerous other aspects are treated on the way, thus providing the reader an instructive overview over diverse quantum mechanical phenomena, e.g. many other potentials, Green's functions, comparison with WKB, calculation of lifetimes and sojourn times, derivation of generating functions, the Coulomb problem in various coordinates, etc. All calculations are given in detail, so that the reader can follow every step.
Introduction To Quantum Mechanics Schr Dinger Equation And Path Integral
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Author : Harald J.W. Müller-Kirsten
language : en
Publisher:
Release Date : 2006
Introduction To Quantum Mechanics Schr Dinger Equation And Path Integral written by Harald J.W. Müller-Kirsten and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Introduction To Path Integral Methods In Physics And Polymer Science
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Author : Frederik W. Wiegel
language : en
Publisher: World Scientific
Release Date : 1986
Introduction To Path Integral Methods In Physics And Polymer Science written by Frederik W. Wiegel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.
This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman. After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.
Introduction To Quantum Field Theory
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Author : V.lG. Kiselev
language : en
Publisher: CRC Press
Release Date : 2000-11-17
Introduction To Quantum Field Theory written by V.lG. Kiselev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-17 with Science categories.
This text explains the features of quantum and statistical field systems that result from their field-theoretic nature and are common to different physical contexts. It supplies the practical tools for carrying out calculations and discusses the meaning of the results. The central concept is that of effective action (or free energy), and the main technical tool is the path integral, although other formalisms are also mentioned. The author emphasizes the simplest models first, then progresses to discussions of real systems before addressing more general and rigorous conclusions. The book is structured around carefully selected problems, which are solved in detail.
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets
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Author : Hagen Kleinert
language : en
Publisher: World Scientific Publishing Company
Release Date : 2006-07-19
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets written by Hagen Kleinert 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 2006-07-19 with Science categories.
This is the fourth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman–Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with 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 given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions. The author's other book on ‘Critical Properties of φ4 Theories’ gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets
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Author : Hagen Kleinert
language : en
Publisher: World Scientific Publishing Company
Release Date : 2006
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets written by Hagen Kleinert 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 2006 with Mathematics categories.
This is the fourth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions.The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals.Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders.Special attention is devoted to path integrals with 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 given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.The author's other book on 'Critical Properties of φ4 Theories' gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.
Feynman Path Integrals In Quantum Mechanics And Statistical Physics
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Author : Lukong Cornelius Fai
language : en
Publisher: CRC Press
Release Date : 2021-04-16
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 2021-04-16 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.
Trajectories And Rays The Path Summation In Quantum Mechanics And Optics I
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Author : M Cetica
language : en
Publisher: World Scientific
Release Date : 1990-12-10
Trajectories And Rays The Path Summation In Quantum Mechanics And Optics I written by M Cetica and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-10 with Science categories.
This book presents selected topics about the path-integral method in Quantum Mechanics and Optics. Starting from an introduction to the grounds of functional integration theory, the main arguments of quantum and statistical mechanics, where the path-integral method works, are exposed. In particular, the partition function, the concept of instanton, tunneling and dissipative phenomena are analysed. The final section is devoted to selected and solved problems. This volume will be useful to beginners as well as more advanced students and researchers in the field.
Mathematical Theory Of Feynman Path Integrals
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Author : Sergio Albeverio
language : en
Publisher: Springer
Release Date : 2008-05-06
Mathematical Theory Of Feynman Path Integrals written by Sergio Albeverio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-06 with Mathematics categories.
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.