Semi Classical Approximation In Quantum Mechanics

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Semi Classical Approximation In Quantum Mechanics

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Author : Victor P. Maslov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30

Semi Classical Approximation In Quantum Mechanics written by Victor P. Maslov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-30 with Science categories.

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.

Semi Classical Approximation In Quantum Mechanics

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Author : Viktor Pavlovich Maslov
language : en
Publisher:
Release Date : 1981

Semi Classical Approximation In Quantum Mechanics written by Viktor Pavlovich Maslov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Approximation theory categories.

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

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Author : V. P. Maslov
language : en
Publisher:
Release Date : 1981

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 has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.

Semiclassical Theory Of Shape Resonances In Quantum Mechanics

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Author : Peter D. Hislop
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Semiclassical Theory Of Shape Resonances In Quantum Mechanics written by Peter D. Hislop and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

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.

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets

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Author : Hagen Kleinert
language : en
Publisher: World Scientific
Release Date : 2004

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets written by Hagen Kleinert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.

This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman -- Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbationexpansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chem-Simons theory of particles with fractional statistics (anyohs) is introduced and applied to explain the fractional quantum Hall effect. The relevance of path integrals to financial markets is discussed, and improvements of the famous Black -- Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.

Semiclassical Physics

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Author : Matthias Brack
language : en
Publisher: CRC Press
Release Date : 2018-03-05

Semiclassical Physics written by Matthias Brack and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Science categories.

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.

Spectral Asymptotics In The Semi Classical Limit

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Author : Mouez Dimassi
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-16

Spectral Asymptotics In The Semi Classical Limit written by Mouez Dimassi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-16 with Mathematics categories.

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.

Semiclassical Analysis

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Author : Maciej Zworski
language : en
Publisher: American Mathematical Society
Release Date : 2022-05-09

Semiclassical Analysis written by Maciej Zworski and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-09 with Mathematics categories.

This book is an excellent, comprehensive introduction to semiclassical analysis. I believe it will become a standard reference for the subject. —Alejandro Uribe, University of Michigan Semiclassical analysis provides PDE techniques based on the classical-quantum (particle-wave) correspondence. These techniques include such well-known tools as geometric optics and the Wentzel–Kramers–Brillouin approximation. Examples of problems studied in this subject are high energy eigenvalue asymptotics and effective dynamics for solutions of evolution equations. From the mathematical point of view, semiclassical analysis is a branch of microlocal analysis which, broadly speaking, applies harmonic analysis and symplectic geometry to the study of linear and nonlinear PDE. The book is intended to be a graduate level text introducing readers to semiclassical and microlocal methods in PDE. It is augmented in later chapters with many specialized advanced topics which provide a link to current research literature.

Finite Mathematics As The Foundation Of Classical Mathematics And Quantum Theory

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Author : Felix Lev
language : en
Publisher: Springer Nature
Release Date : 2020-11-03

Finite Mathematics As The Foundation Of Classical Mathematics And Quantum Theory written by Felix Lev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-03 with Science categories.

This book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved.

Quantum Chemistry And Dynamics Of Excited States

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Author : Leticia González
language : en
Publisher: John Wiley & Sons
Release Date : 2020-11-10

Quantum Chemistry And Dynamics Of Excited States written by Leticia González and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-10 with Science categories.

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.