Wave Packet Analysis Of Feynman Path Integrals

Author : Fabio Nicola,S. Ivan Trapasso
Publisher : Springer Nature
Page : 220 pages
File Size : 43,8 Mb
Release : 2022-07-28
Category : Science
ISBN : 9783031061868

Get Book

Wave Packet Analysis of Feynman Path Integrals by Fabio Nicola,S. Ivan Trapasso Pdf

The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.

Author : Akira Inomata,Hiroshi Kuratsuji,Christopher C. Gerry
Publisher : World Scientific
Page : 338 pages
File Size : 46,6 Mb
Release : 1992
Category : Science
ISBN : 9810206569

Get Book

Path Integrals and Coherent States of SU(2) and SU(1,1) by Akira Inomata,Hiroshi Kuratsuji,Christopher C. Gerry Pdf

The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals on SU(2) and SU(1, 1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problem in curved space and others.The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent states, formulation of coherent path integrals for spin and unitary spin, and semiclassical quantization are presented. Applications are made to the study of quantum fluctuation, the nonlinear field model and phase holonomy.The final chapters present the theory of the SU(1, 1) coherent states and their applications. The radial coulomb problem, the Morse oscillator, and the large-N approximation are discussed. Applications to problems in quantum optics such as squeezed states, interaction with the squeezed vacuum states, and phase operator formalism are also included.This book will be useful as an introduction to the subject as well as a valuable work of reference.

Author : Sonia Mazzucchi
Publisher : World Scientific
Page : 360 pages
File Size : 53,7 Mb
Release : 2021-11-16
Category : Science
ISBN : 9789811214806

Get Book

Mathematical Feynman Path Integrals And Their Applications (Second Edition) by Sonia Mazzucchi Pdf

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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,7 Mb
Release : 2024-06-25
Category : Electronic
ISBN : 9789814507448

Get Book

Trajectories and Rays: The Path-Summation in Quantum Mechanics and Optics I by Anonim Pdf

Author : Kazuo Fujikawa,Hiroshi Suzuki
Publisher : Oxford University Press
Page : 297 pages
File Size : 54,6 Mb
Release : 2004-04-29
Category : Mathematics
ISBN : 9780198529132

Get Book

Path Integrals and Quantum Anomalies by Kazuo Fujikawa,Hiroshi Suzuki Pdf

The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. The path integral formulation of quantum anomalies, i.e. the quantum breaking of certain symmetries, can now cover all the known quantum anomalies in a coherent manner. In this book the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies. No previous knowledge of fieldtheory beyond the advanced undergraduate quantum mechanics is assumed. The book provides the first coherent introductory treatment of the path integral formulation of chiral and Weyl anomalies, with applications to gauge theory in two and four dimensions, conformal field theory and string theory. Explicitand elementary path integral calculations of most of the quantum anomalies covered are given. The conceptual basis of the path integral bosonization in two-dimensional theory, which may have applications to condensed matter theory, for example, is clarified. The book also covers the recent interesting developments in the treatment of fermions and chiral anomalies in lattice gauge theory.

Author : Christoph Thiele
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 47,7 Mb
Release : 2006
Category : Linear operators
ISBN : 9780821836613

Get Book

Wave Packet Analysis by Christoph Thiele Pdf

The concept of ``wave packet analysis'' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L2$ functions. It was later used by Lacey and Thiele to prove bounds on the bilinear Hilbert transform. For quite some time, Carleson's wave packet analysis was thought to be an important idea, but that it had limited applications. But in recent years, it has become clear that this is an important tool for a number of other applications. This book isan introduction to these tools. It emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development. However, the book closes with a dedicated chapter on more recent results. Carleson's original theorem is sometimes cited as one of the most importantdevelopments of 20th century harmonic analysis. The set of ideas stemming from his proof is now seen as an essential element in modern harmonic analysis. Indeed, Thiele won the Salem prize jointly with Michael Lacey for work in this area. The book gives a nice survey of important material, such as an overview of the theory of singular integrals and wave packet analysis itself. There is a separate chapter on ``further developments'', which gives a broader view on the subject, though it does notexhaust all ongoing developments.

Author : Richard P. Feynman,Albert R. Hibbs,Daniel F. Styer
Publisher : Courier Corporation
Page : 386 pages
File Size : 45,8 Mb
Release : 2010-07-21
Category : Science
ISBN : 9780486477220

Get Book

Quantum Mechanics and Path Integrals by Richard P. Feynman,Albert R. Hibbs,Daniel F. Styer Pdf

Looks at quantum mechanics, covering such topics as perturbation method, statistical mechanics, path integrals, and quantum electrodynamics.

Author : Martin C. Gutzwiller
Publisher : World Scientific Publishing Company
Page : 484 pages
File Size : 48,8 Mb
Release : 1986
Category : Integrals, Path
ISBN : UCAL:B4422923

Get Book

Path Integrals from MeV to MeV by Martin C. Gutzwiller Pdf

Author : Jean Zinn-Justin
Publisher : OUP Oxford
Page : 335 pages
File Size : 52,5 Mb
Release : 2004-11-19
Category : Science
ISBN : 9780191581427

Get Book

Path Integrals in Quantum Mechanics by Jean Zinn-Justin Pdf

The main goal of this work is to familiarize the reader with a tool, the path integral, that offers an alternative point of view on quantum mechanics, but more important, under a generalized form, has become the key to a deeper understanding of quantum field theory and its applications, which extend from particle physics to phase transitions or properties of quantum gases. Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual integrals, but have new properties from the viewpoint of analysis. Path integrals are powerful tools for the study of quantum mechanics, because they emphasize very explicitly the correspondence between classical and quantum mechanics. Physical quantities are expressed as averages over all possible paths but, in the semi-classical limit, the leading contributions come from paths close to classical paths. Thus, path integrals lead to an intuitive understanding and simple calculations of physical quantities in the semi-classical limit. We will illustrate this observation with scattering processes, spectral properties or barrier penetration. The formulation of quantum mechanics based on path integrals, if it seems mathematically more complicated than the usual formulation based on partial differential equations, is well adapted to systems with many degrees of freedom, where a formalism of Schrödinger type is much less useful. It allows a simple construction of a many-body theory both for bosons and fermions.

Author : Michio Masujima
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 49,7 Mb
Release : 2008-11-21
Category : Science
ISBN : 9783540878513

Get Book

Path Integral Quantization and Stochastic Quantization by Michio Masujima Pdf

In this book, we discuss the path integral quantization and the stochastic quantization of classical mechanics and classical field theory. Forthe description ofthe classical theory, we have two methods, one based on the Lagrangian formalism and the other based on the Hamiltonian formal ism. The Hamiltonian formalism is derived from the Lagrangian·formalism. In the standard formalism ofquantum mechanics, we usually make use ofthe Hamiltonian formalism. This fact originates from the following circumstance which dates back to the birth of quantum mechanics. The first formalism ofquantum mechanics is Schrodinger's wave mechan ics. In this approach, we regard the Hamilton-Jacobi equation of analytical mechanics as the Eikonal equation of "geometrical mechanics". Based on the optical analogy, we obtain the Schrodinger equation as a result ofthe inverse of the Eikonal approximation to the Hamilton-Jacobi equation, and thus we arrive at "wave mechanics". The second formalism ofquantum mechanics is Heisenberg's "matrix me chanics". In this approach, we arrive at the Heisenberg equation of motion from consideration of the consistency of the Ritz combination principle, the Bohr quantization condition and the Fourier analysis of a physical quantity. These two formalisms make up the Hamiltonian.formalism of quantum me chanics.

Author : Richard Phillips Feynman
Publisher : Unknown
Page : 0 pages
File Size : 47,9 Mb
Release : 1965
Category : Quantum theory
ISBN : 0071139486

Get Book

Quantum Mechanics and Path Integrals [by] R.P. Feynman [and] A.R. Hibbs by Richard Phillips Feynman Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,8 Mb
Release : 2024-06-25
Category : Electronic
ISBN : 9789814469272

Get Book

Mathematical Feynman Path Integrals and Their Applications by Anonim Pdf

Author : M.B Mensky
Publisher : CRC Press
Page : 212 pages
File Size : 52,8 Mb
Release : 1993-01-01
Category : Science
ISBN : 0750302283

Get Book

Continuous Quantum Measurements and Path Integrals by M.B Mensky Pdf

Advances in technology are taking the accuracy of macroscopic as well as microscopic measurements close to the quantum limit, for example, in the attempts to detect gravitational waves. Interest in continuous quantum measurements has therefore grown considerably in recent years. Continuous Quantum Measurements and Path Integrals examines these measurements using Feynman path integrals. The path integral theory is developed to provide formulae for concrete physical effects. The main conclusion drawn from the theory is that an uncertainty principle exists for processes, in addition to the familiar one for states. This implies that a continuous measurement has an optimal accuracy-a balance between inefficient error and large quantum fluctuations (quantum noise). A well-known expert in the field, the author concentrates on the physical and conceptual side of the subject rather than the mathematical.

Author : M.B Mensky
Publisher : CRC Press
Page : 188 pages
File Size : 40,6 Mb
Release : 2017-10-19
Category : Science
ISBN : 9781351458030

Get Book

Continuous Quantum Measurements and Path Integrals by M.B Mensky Pdf

Advances in technology are taking the accuracy of macroscopic as well as microscopic measurements close to the quantum limit, for example, in the attempts to detect gravitational waves. Interest in continuous quantum measurements has therefore grown considerably in recent years. Continuous Quantum Measurements and Path Integrals examines these measurements using Feynman path integrals. The path integral theory is developed to provide formulae for concrete physical effects. The main conclusion drawn from the theory is that an uncertainty principle exists for processes, in addition to the familiar one for states. This implies that a continuous measurement has an optimal accuracy-a balance between inefficient error and large quantum fluctuations (quantum noise). A well-known expert in the field, the author concentrates on the physical and conceptual side of the subject rather than the mathematical.

Author : P. Exner
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400952072

Get Book

Open Quantum Systems and Feynman Integrals by P. Exner Pdf

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.