Semi Classical Approximation In Quantum Mechanics
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Author | : Victor P. Maslov |
Publisher | : Springer Science & Business Media |
Total Pages | : 320 |
Release | : 2001-11-30 |
Genre | : Science |
ISBN | : 9781402003066 |
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.
Author | : Viktor Pavlovich Maslov |
Publisher | : |
Total Pages | : 301 |
Release | : 1981 |
Genre | : Approximation theory |
ISBN | : |
Author | : V. P. Maslov |
Publisher | : |
Total Pages | : |
Release | : 1981 |
Genre | : |
ISBN | : |
Author | : D.. Robert |
Publisher | : |
Total Pages | : 80 |
Release | : 1997 |
Genre | : |
ISBN | : |
Author | : Eric J. Heller |
Publisher | : Princeton University Press |
Total Pages | : 473 |
Release | : 2018-06-05 |
Genre | : Science |
ISBN | : 1400890292 |
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
Author | : Peter D. Hislop |
Publisher | : American Mathematical Soc. |
Total Pages | : 133 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : 0821824627 |
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.
Author | : Matthias Brack |
Publisher | : CRC Press |
Total Pages | : 484 |
Release | : 2018-03-05 |
Genre | : Science |
ISBN | : 0429971370 |
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.
Author | : Eric J. Heller |
Publisher | : Princeton University Press |
Total Pages | : 472 |
Release | : 2018-06-05 |
Genre | : Science |
ISBN | : 0691163731 |
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
Author | : Mouez Dimassi |
Publisher | : Cambridge University Press |
Total Pages | : 243 |
Release | : 1999-09-16 |
Genre | : Mathematics |
ISBN | : 0521665442 |
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author | : M. S. Child |
Publisher | : OUP Oxford |
Total Pages | : 495 |
Release | : 2014-08-21 |
Genre | : Science |
ISBN | : 0191653853 |
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.