Download or read book Semi Classical Approximation in Quantum Mechanics written by Victor P. Maslov and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. The book is, in fact, an extension and continuation of the authors' works [59], [60], [65]. The basic ideas are summarized in the Introduction. The book consists of two parts. In the first, the theory of the canonical operator is develop ed, whereas, in the second, many applications of the canonical operator method to concrete problems of mathematical physics are presented. The authors are pleased to express their deep gratitude to S. M. Tsidilin for his valuable comments. THE AUTHORS IX INTRODUCTION 1. Various problems of mathematical and theoretical physics involve partial differential equations with a small parameter at the highest derivative terms. For constructing approximate solutions of these equations, asymptotic methods have long been used. In recent decades there has been a renaissance period of the asymptotic methods of linear mathematical physics. The range of their applicability has expanded: the asymptotic methods have been not only continuously used in traditional branches of mathematical physics but also have had an essential impact on the development of the general theory of partial differential equations. It appeared recently that there is a unified approach to a number of problems which, at first sight, looked rather unrelated.
Download or read book Semi classical Approximation in Quantum Mechanics written by Viktor Pavlovich Maslov and published by . This book was released on 1981 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book V P Maslov and M V Fedroiuk Semi classical approximation in quantum mechanics Kvaziklassi eskoe pribli enie dlja uravnenij kvantovoj mechaniki engl Transl from the Russian by J Niederle and J Tolar written by V. P. Maslov and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semi classical Approximation in Quantum Mechanics written by D.. Robert and published by . This book was released on 1997 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semiclassical Theory of Shape Resonances in Quantum Mechanics written by Peter D. Hislop and published by American Mathematical Soc.. This book was released on 1989 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we prove the existence of shape resonances in the semi-classical approximation for Hamiltonians of the form [italic]H([lowercase Greek]Lambda) [triple bar symbol] −([capital Greek]Delta + ([lowercase Greek]Lambda2[italic]V + [italic]U on [italic]L2([bold]R[superscript italic]n), where ([lowercase Greek]Lambda [triple bar symbol] 1/h[with stroke], h[with stroke] [triple bar symbol] (2[lowercase Greek]Pi)−1h.
Download or read book Semiclassical Physics written by Matthias Brack and published by CRC Press. This book was released on 2018-03-05 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book attempts to convey to the reader that semiclassical physics can be fun, as well as useful for understanding quantum fluctuations in interacting many-body systems. It presents applications to finite fermion systems in diverse areas of physics.
Download or read book The Semiclassical Way to Dynamics and Spectroscopy written by Eric J. Heller and published by Princeton University Press. This book was released on 2018-06-05 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level text that examines the semiclassical approach to quantum mechanics Physical systems have been traditionally described in terms of either classical or quantum mechanics. But in recent years, semiclassical methods have developed rapidly, providing deep physical insight and computational tools for quantum dynamics and spectroscopy. In this book, Eric Heller introduces and develops this subject, demonstrating its power with many examples. In the first half of the book, Heller covers relevant aspects of classical mechanics, building from them the semiclassical way through the semiclassical limit of the Feynman path integral. The second half of the book applies this approach to various kinds of spectroscopy, such as molecular spectroscopy and electron imaging and quantum dynamical systems with an emphasis on tunneling. Adopting a distinctly time-dependent viewpoint, Heller argues for semiclassical theories from experimental and theoretical vantage points valuable to research in physics and chemistry. Featuring more than two hundred figures, the book provides a geometric, phase-space, and coordinate-space pathway to greater understanding. Filled with practical examples and applications, The Semiclassical Way to Dynamics and Spectroscopy is a comprehensive presentation of the tools necessary to successfully delve into this unique area of quantum mechanics. A comprehensive approach for using classical mechanics to do quantum mechanics More than two hundred figures to assist intuition Emphasis on semiclassical Green function and wave packet perspective, as well as tunneling and spectroscopy Chapters include quantum mechanics of classically chaotic systems, quantum scarring, and other modern dynamical topics
Download or read book Semiclassical Mechanics with Molecular Applications written by M. S. Child and published by OUP Oxford. This book was released on 2014-08-21 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of an established graduate text, this book complements the material for a typical advanced graduate course in quantum mechanics by showing how the underlying classical structure is reflected in quantum mechanical interference and tunnelling phenomena, and in the energy and angular momentum distributions of quantum mechanical states in the moderate to large (10-100) quantum number regime. Applications include accurate quantization techniques for a variety of tunnelling and curve-crossing problems and of non-separable bound systems; direct inversion of molecular scattering and spectroscopic data; wavepacket propagation techniques; and the prediction and interpretation of elastic, inelastic and chemically reactive scattering. The main text concentrates less on the mathematical foundations than on the global influence of the classical phase space structures on the quantum mechanical observables. Further mathematical detail is contained in the appendices and worked problem sets are included as an aid to the student.
Download or read book Spectral Asymptotics in the Semi Classical Limit written by Mouez Dimassi and published by Cambridge University Press. This book was released on 1999-09-16 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Download or read book An Introduction to Semiclassical and Microlocal Analysis written by André Bach and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semi-classical theory.
Download or read book KAM Theory and Semiclassical Approximations to Eigenfunctions written by Vladimir F. Lazutkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a surprising fact that so far almost no books have been published on KAM theory. The first part of this book seems to be the first monographic exposition of this subject, despite the fact that the discussion of KAM theory started as early as 1954 (Kolmogorov) and was developed later in 1962 by Arnold and Moser. Today, this mathematical field is very popular and well known among physicists and mathematicians. In the first part of this Ergebnisse-Bericht, Lazutkin succeeds in giving a complete and self-contained exposition of the subject, including a part on Hamiltonian dynamics. The main results concern the existence and persistence of KAM theory, their smooth dependence on the frequency, and the estimate of the measure of the set filled by KAM theory. The second part is devoted to the construction of the semiclassical asymptotics to the eigenfunctions of the generalized Schrödinger operator. The main result is the asymptotic formulae for eigenfunctions and eigenvalues, using Maslov`s operator, for the set of eigenvalues of positive density in the set of all eigenvalues. An addendum by Prof. A.I. Shnirelman treats eigenfunctions corresponding to the "chaotic component" of the phase space.
Download or read book On the Semi Classical Expansion in Quantum Mechanics for Arbitrary Hamiltonians written by Maurice M. Mizrahi and published by . This book was released on 1976 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to extend to a very wide class of Hamiltonians the range of validity of a well-known and oft-used expression for the semi-classical (WKB) approximation to the quantum-mechanical propagator K((q sub b), (t sub b);(q sub a), (t sub a)) identically equal to ((q sub a), (t sub b)/(q sub a), (t sub a)), or probability amplitude that a particle at (q sub a) at time (t sub a) will arrive at (q sub b) at time (t sub b).
Download or read book Advanced Quantum Mechanics written by Reinhold Blümel and published by Jones & Bartlett Learning. This book was released on 2011-08-24 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics
Download or read book John David Jackson written by John David Jackson and published by John Wiley & Sons. This book was released on 2023-08-31 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Quantum Mechanics Unique graduate-level textbook on quantum mechanics by John David Jackson, author of the renowned Classical Electrodynamics A Course in Quantum Mechanics is drawn directly from J. D. Jackson’s detailed lecture notes and problem sets. It is edited by his colleague and former student Robert N. Cahn, who has taken care to preserve Jackson’s unique style. The textbook is notable for its original problems focused on real applications, with many addressing published data in accompanying tables and figures. Solutions are provided for problems that are critical for understanding the material and that lead to the most important physical consequences. Overall, the text is comprehensive and comprehensible; derivations and calculations come with clearly explained steps. More than 120 figures illustrate underlying principles, experimental apparatus, and data. In A Course in Quantum Mechanics readers will find detailed treatments of: Wave mechanics of de Broglie and Schrödinger, the Klein-Gordon equation and its non-relativistic approximation, free particle probability current, expectation values. Schrödinger equation in momentum space, spread in time of a free-particle wave packet, density matrix, Sturm-Liouville eigenvalue problem. WKB formula for bound states, example of WKB with a power law potential, normalization of WKB bound state wave functions, barrier penetration with WKB. Rotations and angular momentum, representations, Wigner d-functions, addition of angular momenta, the Wigner-Eckart theorem. Time-independent perturbation theory, Stark, Zeeman, Paschen-Back effects, time-dependent perturbation theory, Fermi’s Golden Rule. Atomic structure, helium, multiplet structure, Russell-Saunders coupling, spin-orbit interaction, Thomas-Fermi model, Hartree-Fock approximation. Scattering amplitude, Born approximation, allowing internal structure, inelastic scattering, optical theorem, validity criterion for the Born approximation, partial wave analysis, eikonal approximation, resonance. Semi-classical and quantum electromagnetism, Aharonov-Bohm effect, Lagrangian and Hamiltonian formulations, gauge invariance, quantization of the electromagnetic field, coherent states. Emission and absorption of radiation, dipole transitions, selection rules, Weisskopf-Wigner treatment of line breadth and level shift, Lamb shift. Relativistic quantum mechanics, Klein-Gordon equation, Dirac equation, two-component reduction, hole theory, Foldy-Wouthuysen transformation, Lorentz covariance, discrete symmetries, non-relativistic and relativistic Compton scattering.
Download or read book Quantum and Semiclassical Trajectories Development and Applications written by Yujun Zheng and published by Frontiers Media SA. This book was released on 2023-08-02 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classical Semiclassical and Quantum Dynamics in Atoms written by Harald Friedrich and published by Springer. This book was released on 1997-06-19 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content Description #Includes bibliographical references and index.
Download or read book Quantum Mechanics written by Kenichi Konishi and published by Oxford University Press. This book was released on 2009-03-05 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern and comprehensive textbook intended to correct the lack of such a text in times of the ever-increasing importance of the subject in contemporary science, technology, and everyday life. With its clear pedagogical presentation and with many examples and solved problems it is useful for physics students, researchers and teachers alike.
