Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics

Front Cover
Springer Science & Business Media, May 28, 2006 - Mathematics - 408 pages

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.

 

Contents

The Phase Space Route to the Hydrodynamic Equations
3
The Bohmian Route to the Hydrodynamic Equations
40
Phase Spaces
85
Function and Derivative Approximation on Unstructured Grids
123
Applications of the Quantum Trajectory Method
148
Adaptive Methods for Trajectory Dynamics
166
Quantum Trajectories for Multidimensional Dynamics
190
Approximations to the Quantum Force
218
Quantum Trajectories in Phase Space
254
Mixed QuantumClassical Dynamics
300
The Stress Tensor
322
Quantum Trajectories for Stationary States
354
Challenges and Opportunities
369
Atomic Units
389
150
402
Copyright

Derivative Propagation Along Quantum Trajectories
235

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