عنوان

The semiclassical way to dynamics and spectroscopy /

1400890292

9781400890293

0691163731

9780691163734

The semiclassical way to dynamics and spectroscopy /

[Book]

Eric J. Heller.

Princeton :

Princeton University Press,

2018.

1 online resource (473 pages)

Includes bibliographical references (pages [439]-448) and index.

Cover; Title; Copyright; Dedication; Contents; Preface; Acknowledgments; Introduction; PART I CLASSICAL MECHANICS WITH AN EYE TO QUANTUM MECHANICS; Chapter 1 The Lagrangian and the Action; 1.1 Extremal Action and Equations of Motion; 1.2 Form of the Lagrangian; 1.3 Noether's Theorem; 1.4 Hamiltonian Formulation; 1.5 Constrained Systems and Forces of Constraint; 1.6 Derivatives and Legendre Transformations of the Action; 1.7 Velocity-Dependent Potentials; Chapter 2 Canonical Transformations; 2.1 Hamilton-Jacobi Idea; 2.2 Action as the Generating Function for Dynamics.

2.3 Phase Space and Canonical Transformations2.4 Transformation of Manifolds, Areas, and Densities; Chapter 3 Time Evolution in Phase Space; 3.1 Time Evolution of Point Trajectories; 3.2 Generating Functions and Joint Probabilities; 3.3 Poincaré-Cartan Invariants; 3.4 Poincaré Surface of Section; 3.5 Action-Angle Coordinates; 3.6 Area-Preserving Maps; 3.7 Poincaré-Birkhoff Fixed-Point Theorem; 3.8 Stability Analysis; 3.9 Motion near a Periodic Orbit; 3.10 Classical Baker's Map; 3.11 (Classical) Trace of a Periodic Orbit; 3.12 Survival of (Most of) the Tori under Weak Interactions.

3.13 Structure of Phase SpaceChapter 4 Classical Resonance Theory; 4.1 Paradigm System: Linearly Forced, Damped Oscillator; 4.2 Slow External Time-Dependent Perturbations; 4.3 Fast External Time-Dependent Perturbations; 4.4 Averaging of Perturbations; 4.5 Resonance Characteristics and Removal; 4.6 Resonance and Classical Perturbation Theory; 4.7 Oscillator Connection; PART II QUANTUM AND SEMICLASSICAL MECHANICS; Chapter 5 Aspects of Time-Dependent Quantum Mechanics; 5.1 Time-Dependent Perturbation Theory; 5.2 Fermi Golden Rule for Decay and Beyond.

5.3 System-Bath Interactions, Dephasing, and Depopulation5.4 Eigenstates as Fourier Transform of Dynamics; Chapter 6 Stationary Phase Integration; 6.1 One Dimension; 6.2 Example: Airy Function and Linear Ramp Potential; 6.3 Classically Forbidden (Tunneling) Region; 6.4 Kirchhoff Method; 6.5 Kirchhoff Method, Rough Surfaces, and Evanescent Waves; Chapter 7 Feynman Path Integral to Van Vleck Propagator; 7.1 Semiclassical Program; 7.2 Dynamical Postulate of Quantum Dynamics; 7.3 Feynman Path Integral; 7.4 Van Vleck-Morette-Gutzwiller Semiclassical Propagator.

7.5 Another Route to the Van Vleck-Morette-Gutzwiller Propagator7.6 Semiclassical Energy Green Function; 7.7 Trace Formula for the Energy Spectrum; 7.8 Closed Orbits for Spectroscopy; 7.9 History; Chapter 8 Stressing the VVMG Propagator; 8.1 Semiclassical Wavepacket Dynamics in an Anharmonic Oscillator; 8.2 Quantum and Semiclassical Revival; 8.3 Autocorrelation and Spectrum in a Chaotic System; 8.4 Anderson Localization; Chapter 9 Phase Space Representations of Wavefunctions and Densities; 9.1 Wigner Phase Space; 9.2 Quantum Flux; 9.3 Husimi Phase Space and Related Distributions; Chapter 10 Gaussian Wavepackets and Linear Dynamics.

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A graduate-level text that examines the semiclassical approach to quantum mechanicsPhysical 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 mechanicsMore than two hundred figures to assist intuitionEmphasis on semiclassical Green function and wave packet perspective, as well as tunneling and spectroscopyChapters include quantum mechanics of classically chaotic systems, quantum scarring, and other modern dynamical topics.

JSTOR

22573/ctvc618cm

Semiclassical Way to Dynamics and Spectroscopy.

9780691163734

Quantum theory.

Quantum theory.

SCIENCE-- Chemistry-- Physical & Theoretical.

SCIENCE-- Energy.

SCIENCE-- Mechanics-- General.

SCIENCE-- Physics-- General.

SCI-- 013050

SCI-- 018000

SCI-- 024000

SCI-- 041000

SCI-- 055000

SCI-- 057000

SCI-- 078000

Heller, Eric Johnson.

20200822122902.0

pn

[Book]

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