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.
Trajectory approaches to quantum mechanics.- The Bohm hydrodynamic equations.- The phase space route to the hydrodynamic equations.- Quantum trajectories.- Fitting methods for computation of spatial derivatives.- Applications to wavepacket tunneling and decoherence.- Application to electronic transitions.- The initial value representation and correlation functions- Mixed quantum-classical dynamics.- Moving adaptive grids.- Trajectory approach to the density matrix.- Derivative propagation along quantum trajectories.- Quantum dynamics in phase space.- Non-Bohmain trajectory approaches to quantum mechanics.
This is a rapidly developing field to which the author is a leading contributor
New methods in quantum dynamics and computational techniques, with applications to interesting physical problems, are brought together in this book
Useful to both students and researchers
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.