Download or read book Wave Packet Analysis written by Christoph Thiele and published by American Mathematical Soc.. This book was released on 2006 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Wave Packet Analysis of Feynman Path Integrals written by Fabio Nicola and published by Springer Nature. This book was released on 2022-07-28 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Meaning of the Wave Function written by Shan Gao and published by Cambridge University Press. This book was released on 2017-03-16 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering much of the recent debate, this ambitious text provides new, decisive proof of the reality of the wave function.
Download or read book Wave Packet Analysis of Electron Phonon Interaction in the Wigner Formalism written by and published by . This book was released on 1996 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Chemistry and Dynamics of Excited States written by Leticia González and published by John Wiley & Sons. This book was released on 2021-02-01 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: ● Essential theoretical techniques to describe the properties and dynamics of chemical systems ● Electronic Structure methods for stationary calculations ● Methods for electronic excited states from both a quantum chemical and time-dependent point of view ● A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.
Download or read book Femtochemistry written by Ahmed H. Zewail and published by World Scientific. This book was released on 1994 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes on Femtochemistry present a timely contribution to a field central to the understanding of the dynamics of the chemical bond. This century has witnessed great strides in time and space resolutions, down to the atomic scale, providing chemists, biologists and physicists with unprecedented opportunities for seeing microscopic structures and dynamics. Femtochemistry is concerned with the time resolution of the most elementary motions of atoms during chemical change -- bond breaking and bond making -- on the femtosecond (10-15 second) time scale. This atomic scale of time resolution has now reached the ultimate for the chemical bond and as Lord George Porter puts it, chemists are near the end of the race against time. These two volumes cover the general concepts, techniques and applications of femtochemistry.Professor Ahmed Zewail, who has made the pioneering contributions in this field, has from over 250 publications selected the articles for this anthology. These volumes begin with a commentary and a historical chronology of the milestones. He then presents a broad perspective of the current state of knowledge in femtochemistry by researchers around the world and discusses possible new directions. In the words of a colleague, "it is a must on the reading-list for all of my students ... all readers will find this to be an informative and valuable overview."The introductory articles in Volume I provide reviews for both the non-experts as well as for experts in the field. This is followed by papers on the basic concepts. For applications, elementary reactions are studied first and then complex reactions. Volume I is complete with studies of solvation dynamics, non-reactive systems, ultrafast electron diffraction and the control of chemical reactions.Volume II continues with reaction rates, the concept of elementary intramolecular vibrational-energy redistribution (IVR) and the phenomena of rotational coherence which has become a powerful tool for the determination of molecular structure via time resolution. The second volume ends with an extensive list of references, according to topics, based on work by Professor Zewail and his group at Caltech.These collected works by Professor Zewail will certainly be indispensable to both experts and beginners in the field. The author is known for his clarity and for his creative and systematic contributions. These volumes will be of interest and should prove useful to chemists, biologists and physicists. As noted by Professor J Manz (Berlin) and Professor A W Castleman, Jr. (Penn State): femtochemistry is yielding exciting new discoveries from analysis to control of chemical reactions, with applications in many domains of chemistry and related fields, e.g., physical, organic and inorganic chemistry, surface science, molecular biology, ... etc.
Download or read book Compendium of Quantum Physics written by Daniel Greenberger and published by Springer Science & Business Media. This book was released on 2009-07-25 with total page 901 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Wave Mechanics written by Wolfgang (Physiker) Pauli and published by Courier Corporation. This book was released on 2000-09-18 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on wave functions of force-free particles, description of a particle in a box and in free space, particle in a field of force, multiple particles, eigenvalue problems, more.
Download or read book Tunneling And Its Implications Proceedings Of The Adriatico Research Conference written by D Mugnai and published by World Scientific. This book was released on 1997-04-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tunneling And Its Implications written by Daniela Mugnai and published by World Scientific. This book was released on 1997 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Download or read book Bohmian Mechanics Open Quantum Systems and Continuous Measurements written by Antonio B. Nassar and published by Springer. This book was released on 2017-03-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Trajectory Description of Quantum Processes II Applications written by Ángel S. Sanz and published by Springer. This book was released on 2013-09-13 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Monthly Weather Review written by and published by . This book was released on 2003 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantization and the Wave Packet Transform written by Vladimir E. Nazajkinskij and published by . This book was released on 1999 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Consistent Quantum Theory written by Robert B. Griffiths and published by Cambridge University Press. This book was released on 2003-11-13 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.
Download or read book Spin Wave Confinement written by Sergej O. Demokritov and published by CRC Press. This book was released on 2017-09-07 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of Spin-Wave Confinement, the magnetic community’s interest in dynamic excitations in magnetic systems of reduced dimensions has been increasing. Although the concept of spin waves and their quanta (magnons) as propagating excitation of magnetic media was introduced more than 80 years ago, this field has been repeatedly bringing us fascinating new physical phenomena. The successful development of magnonics as an emerging subfield of spintronics, which considers confined spin waves as a basis for smaller, faster, more robust, and more power-efficient electronic devices, inevitably demands reduction in the sizes and dimensions of the magnetic systems being studied. The unique features of magnons, including the possibility of carrying spin information over relatively long distances, the possibility of achieving submicrometer wavelength at microwave frequencies, and controllability by electronic signal via magnetic fields, make magnonic devices distinctively suited for implementation of novel integrated electronic schemes characterized by high speed, low power consumption, and extended functionalities. Edited by S. O. Demokritov, a prominent magnonics researcher who has successfully collected the results of cutting-edge research by almost all main players in the field, this book is for everyone involved in nanotechnology, spintronics, magnonics, and nanomagnetism.
Download or read book An Introduction to Quantum Theory written by Frank S. Levin and published by Cambridge University Press. This book was released on 2002 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate introductory quantum mechanics textbook with a large number of figures and exercises.
