Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics

Robert E. Wyatt (auth.)0387229647, 9780387229645, 9780387281452

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

Table of contents :
Introduction to Quantum Trajectories….Pages 1-39
The Bohmian Route to the Hydrodynamic Equations….Pages 40-61
The Phase Space Route to the Hydrodynamic Equations….Pages 62-88
The Dynamics and Properties of Quantum Trajectories….Pages 89-122
Function and Derivative Approximation on Unstructured Grids….Pages 123-147
Applications of the Quantum Trajectory Method….Pages 148-165
Adaptive Methods for Trajectory Dynamics….Pages 166-189
Quantum Trajectories for Multidimensional Dynamics….Pages 190-217
Approximations to the Quantum Force….Pages 218-234
Derivative Propagation Along Quantum Trajectories….Pages 235-253
Quantum Trajectories in Phase Space….Pages 254-299
Mixed Quantum-Classical Dynamics….Pages 300-321
Topics in Quantum Hydrodynamics: The Stress Tensor and Vorticity….Pages 322-353
Quantum Trajectories for Stationary States….Pages 354-368
Challenges and Opportunities….Pages 369-388