Wave Packet Analysis
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Author | : Christoph Thiele |
Publisher | : American Mathematical Soc. |
Total Pages | : 97 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821836617 |
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 | : Fabio Nicola |
Publisher | : Springer Nature |
Total Pages | : 220 |
Release | : 2022-07-28 |
Genre | : Science |
ISBN | : 3031061861 |
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 | : Shan Gao |
Publisher | : Cambridge University Press |
Total Pages | : 201 |
Release | : 2017-03-16 |
Genre | : Science |
ISBN | : 1107124352 |
Covering much of the recent debate, this ambitious text provides new, decisive proof of the reality of the wave function.
Author | : Daniel Greenberger |
Publisher | : Springer Science & Business Media |
Total Pages | : 901 |
Release | : 2009-07-25 |
Genre | : Science |
ISBN | : 3540706267 |
With contributions by leading quantum physicists, philosophers and historians, this comprehensive A-to-Z of quantum physics provides a lucid understanding of key concepts of quantum theory and experiment. It covers technical and interpretational aspects alike, and includes both traditional and new concepts, making it an indispensable resource for concise, up-to-date information about the many facets of quantum physics.
Author | : |
Publisher | : |
Total Pages | : 20 |
Release | : 1996 |
Genre | : |
ISBN | : |
A theoretical and computational analysis is presented of the motion of a single one-dimensional electron, represented by a wave packet of given average momentum and position, in a fixed potential profile in presence of electron phonon interaction. The electron propagation can take place with or without an external bias. A perturbative approach is used in the theoretical framework of the Wigner function accounting for the continuous quantum dynamical evolution of the scattering process. The unperturbed hamiltonian contains the one-dimensional potential profile and the external field, while the electron phonon coupling potential is considered as the perturbation hamiltonian. Computational results are presented for the case of an electron propagating (1) without applied forces, (2) through a region where a uniform electric field is applied, and (3) in a double barrier potential in resonance conditions due to the relevance of these physical cases for practical applications.
Author | : D Mugnai |
Publisher | : World Scientific |
Total Pages | : 486 |
Release | : 1997-04-19 |
Genre | : |
ISBN | : 9814546984 |
The motion of a particle undergoing quantum tunneling has long been an open and debated problem in several aspects. One of the most discussed is the determination of the time spent in such processes, but many other features deserve consideration. In this volume, both theoretical and experimental aspects, such as quantum measurement, optical analogy, experimental tests, solid state devices and time scale for anomalies (quantum Zeno effect and superluminal evanescence), are explored.
Author | : Daniela Mugnai |
Publisher | : World Scientific |
Total Pages | : 486 |
Release | : 1997 |
Genre | : Tunneling (Physics) |
ISBN | : 9814530352 |
"The motion of a particle undergoing quantum tunneling has long been an open and debated problem in several aspects. One of the most discussed is the determination of the time spent in such processes, but many other features deserve consideration. In this volume, both theoretical and experimental aspects, such as quantum measurement, optical analogy, experimental tests, solid state devices and time scale for anomalies (quantum Zeno effect and superluminal evanescence), are explored."--Publisher's website
Author | : Antonio B. Nassar |
Publisher | : Springer |
Total Pages | : 255 |
Release | : 2017-03-14 |
Genre | : Science |
ISBN | : 3319536532 |
This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from the violation of the noncrossing rule of quantum trajectories.
Author | : Ángel S. Sanz |
Publisher | : Springer |
Total Pages | : 345 |
Release | : 2013-09-13 |
Genre | : Science |
ISBN | : 3642179746 |
Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.
Author | : Vladimir E. Nazajkinskij |
Publisher | : |
Total Pages | : 65 |
Release | : 1999 |
Genre | : |
ISBN | : |