Feynman Integral And Random Dynamics In Quantum Physics PDF Download
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| Author | : Z. Haba |
| Publisher | : Springer |
| Total Pages | : 367 |
| Release | : 2011-10-13 |
| Genre | : Science |
| ISBN | : 9789401147170 |
Download Feynman Integral and Random Dynamics in Quantum Physics Book in PDF, ePub and Kindle
The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics.
| Author | : Z. Haba |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 378 |
| Release | : 2013-03-11 |
| Genre | : Science |
| ISBN | : 9401147167 |
Download Feynman Integral and Random Dynamics in Quantum Physics Book in PDF, ePub and Kindle
The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics.
| Author | : P. Exner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9400952074 |
Download Open Quantum Systems and Feynman Integrals Book in PDF, ePub and Kindle
Every part of physics offers examples of non-stability phenomena, but probably nowhere are they so plentiful and worthy of study as in the realm of quantum theory. The present volume is devoted to this problem: we shall be concerned with open quantum systems, i.e. those that cannot be regarded as isolated from the rest of the physical universe. It is a natural framework in which non-stationary processes can be investigated. There are two main approaches to the treatment of open systems in quantum theory. In both the system under consideration is viewed as part of a larger system, assumed to be isolated in a reasonable approximation. They are differentiated mainly by the way in which the state Hilbert space of the open system is related to that of the isolated system - either by orthogonal sum or by tensor product. Though often applicable simultaneously to the same physical situation, these approaches are complementary in a sense and are adapted to different purposes. Here we shall be concerned with the first approach, which is suitable primarily for a description of decay processes, absorption, etc. The second approach is used mostly for the treatment of various relaxation phenomena. It is comparably better examined at present; in particular, the reader may consult a monograph by E. B. Davies.
| Author | : Richard P. Feynman |
| Publisher | : Courier Corporation |
| Total Pages | : 386 |
| Release | : 2010-07-21 |
| Genre | : Science |
| ISBN | : 0486477223 |
Download Quantum Mechanics and Path Integrals Book in PDF, ePub and Kindle
Looks at quantum mechanics, covering such topics as perturbation method, statistical mechanics, path integrals, and quantum electrodynamics.
| Author | : Gert Roepstorff |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 400 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642578861 |
Download Path Integral Approach to Quantum Physics Book in PDF, ePub and Kindle
Specifically designed to introduce graduate students to the functional integration method in contemporary physics as painlessly as possible, the book concentrates on the conceptual problems inherent in the path integral formalism. Throughout, the striking interplay between stochastic processes, statistical physics and quantum mechanics comes to the fore, and all the methods of fundamental interest are generously illustrated by important physical examples.
| Author | : Richard Phillips Feynman |
| Publisher | : McGraw-Hill Companies |
| Total Pages | : 392 |
| Release | : 1965 |
| Genre | : Science |
| ISBN | : |
Download Quantum Mechanics and Path Integrals Book in PDF, ePub and Kindle
The fundamental concepts of quantum mechanics -- The quantum-mechanical law of motion -- Developing the concepts with special examples -- The Schrödinger description of quantum mechanics -- Measurements and operators -- The perturbation method in quantum mechanics -- Transition elements -- Harmonic oscillators -- Quantum electrodynamics -- Statistical mechanics -- The variational method -- Other problems in probability.
| Author | : Sonia Mazzucchi |
| Publisher | : World Scientific |
| Total Pages | : 360 |
| Release | : 2021-11-16 |
| Genre | : Science |
| ISBN | : 9811214808 |
Download Mathematical Feynman Path Integrals And Their Applications (Second Edition) Book in PDF, ePub and Kindle
Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.
| Author | : Lukong Cornelius Fai |
| Publisher | : CRC Press |
| Total Pages | : 394 |
| Release | : 2021-04-16 |
| Genre | : Science |
| ISBN | : 1000349063 |
Download Feynman Path Integrals in Quantum Mechanics and Statistical Physics Book in PDF, ePub and Kindle
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.
| Author | : Richard Phillips Feynman |
| Publisher | : World Scientific |
| Total Pages | : 142 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 9812563660 |
Download Feynman's Thesis Book in PDF, ePub and Kindle
Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled ?The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space?time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.The result was the path integral approach, which satisfied ? and transcended ? its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space?time viewpoint.The present volume includes Feynman's Princeton thesis, the related review article ?Space?Time Approach to Non-Relativistic Quantum Mechanics? [Reviews of Modern Physics 20 (1948), 367?387], Paul Dirac's seminal paper ?The Lagrangian in Quantum Mechanics'' [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.
| Author | : Kai Lai Chung |
| Publisher | : World Scientific |
| Total Pages | : 228 |
| Release | : 2003 |
| Genre | : Science |
| ISBN | : 9789812384157 |
Download Introduction to Random Time and Quantum Randomness Book in PDF, ePub and Kindle
This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K L Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown. In the second essay J-C Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested.
