Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics

ISBN-13: 9781441919908 / Angielski / Miękka / 2010 / 408 str.

Robert E. Wyatt; Corey J. Trahan

Opis

Remarkable progress has recently been made in the application of quantumtrajectories as the computational tool for solving quantum mechanical problems. This is the first book to present these developments in the broader context of the hydrodynamical formulation of quantum dynamics. In addition to a thorough discussion of the quantum trajectory equations of motion, there is considerable material that deals with phase space dynamics, adaptive moving grids, electronic energy transfer, and trajectories for stationary states. On the pedagogical side, a number of sections of this book will be accessible to students who have had an introductory quantum mechanics course. There is also considerable material for advanced researchers, and chapters in the book cover both methodology and applications. The book will be useful to students and researchers in physics, chemistry, applied math, and computational dynamics.

Recenzje

From the reviews:

"This excellent book covers a wide range of topics associated with Quantum Hydrodynamics. It's an excellent survey of the history, current state-of-the-field, and future research directions." (Brian Kendrick, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA)

"The book is unique in that it addresses with equal expertise, computational methodology and theoretical connections at the interface between de Broglie-Bohm theory and phase space moment methods. A highly didactic text, to be recommended to graduate students and researchers in physics and chemistry." (Irene Burghardt, Dépt. de chimie, Ecole Normale Supérieure, Paris, France)

"Wyatt shows how one can use the ideas drawn from Bohm's interpretation to develop new and efficient computational methods for both time dependent and time independent quantum mechanics.This is THE definitive text on practical Bohmian mechanics." (Eric Bittner, Dept. of Chemistry, University of Houston, TX, USA)

"The book under review is a good introduction to quantum hydrodynamics and an invaluable survey of the subject. It is written in clear and rigorous language and may be helpful both for novices having basic knowledge in quantum mechanics and experts. ... Numerous illustrations, results of numerical computations and historical comments make reading more fascinating." (Sergei A. Nemnyugin, Mathematical Reviews, Issue 2006 k)

"This book presents the state of the art in the quantum trajectory (QT) method and its applications in quantum hydrodynamics. ... In addition to advanced issues at the level of professional researchers, the book also contains many introductory elements that can nicely serve also to graduate students as a suitable extension of their textbook literature on quantum mechanics. Numerous boxes with outlines and summaries of basic results of chapter are particularly valuable to those who need a brief and concise information on a particular item." (Vladimir Cadez, Zentralblatt MATH, Vol. 1107 (9), 2007)

Spis treści

to Quantum Trajectories.- The Bohmian Route to the Hydrodynamic Equations.- The Phase Space Route to the Hydrodynamic Equations.- The Dynamics and Properties of Quantum Trajectories.- Function and Derivative Approximation on Unstructured Grids.- Applications of the Quantum Trajectory Method.- Adaptive Methods for Trajectory Dynamics.- Quantum Trajectories for Multidimensional Dynamics.- Approximations to the Quantum Force.- Derivative Propagation Along Quantum Trajectories.- Quantum Trajectories in Phase Space.- Mixed Quantum-Classical Dynamics.- Topics in Quantum Hydrodynamics: The Stress Tensor and Vorticity.- Quantum Trajectories for Stationary States.- Challenges and Opportunities.

O autorze

Remarkable progress has recently been made in the development and application of quantum trajectories as the computational tool for solving the time dependent Schrodinger equation. Analogous methods for stationary bound states are also being developed. The purpose of this book is to present recent developments and applications of quantum trajectory methods in the broader context of the hydrodynamical formulation of quantum dynamics. While many chapters of the book deal with Lagrangian quantum trajectories in which the velocity matches that of the probability fluid, other chapters deal with what will be termed post-Lagrangian trajectories. There are also many state-of-the-art topics covered that are unique to this book. On the pedagogical side, a number of sections will be accessible to students who have had at least one course in quantum dynamics. There is also considerable material for advanced researchers, and chapters in the book cover both methodology and applications.

Blurb

Remarkable progress has recently been made in the application of quantumtrajectories as the computational tool for solving quantum mechanical problems. This is the first book to present these developments in the broader context of the hydrodynamical formulation of quantum dynamics. In addition to a thorough discussion of the quantum trajectory equations of motion, there is considerable material that deals with phase space dynamics, adaptive moving grids, electronic energy transfer, and trajectories for stationary states.

On the pedagogical side, a number of sections of this book will be accessible to students who have had an introductory quantum mechanics course. There is also considerable material for advanced researchers, and chapters in the book cover both methodology and applications. The book will be useful to students and researchers in physics, chemistry, applied math, and computational dynamics.

"This excellent book covers a wide range of topics associated with Quantum Hydrodynamics.

It's an excellent survey of the history, current state-of-the-field, and future research directions."

Brian Kendrick,Theoretical Division, Los Alamos National Laboratory, Los Alamos,NM, USA

The book is unique in that it addresses with equal expertise, computational methodology and theoretical connections at the interface between de Broglie-Bohm theory and phase space moment methods.A highly didactic text, to be recommended to graduate students and researchers in physics and chemistry.

Irene Burghardt,Departement de chimie, Ecole Normale Superieure, Paris, France

Wyatt shows how one can use the ideas drawn from Bohm's interpretation to develop new and efficient computational methods for both time dependent and time independent quantum mechanics.This is THE definitive text on practical Bohmian mechanics.

Eric Bittner,Department of Chemistry, University of Houston, Tx, USA