Quantum dynamics with trajectories : introduction to quantum hydrodynamics量子动力学与轨迹：量子流体力学概论
点此进入淘宝搜索页搜索分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者： Robert E. Wyatt等著
出 版 社：
出版时间： 2005-5-1字数：版次： 1页数： 405印刷时间： 2005/05/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387229645包装： 精装内容简介
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.
目录
Preface
Outline of Boxes
Historical Comments with Portraits
Sources for Portraits of Physicists
Permissions for Use of Figures
1 Introduction to Quantum Trajectories
1.1 Dynamics with Quantum Trajectories
1.2 Routes to Quantum Trajectories
1.3 The Quantum Trajectory Method
1.4 Derivative Evaluation on Unstructured Grids
1.5 Applications of the Quantum Trajectory Method
1.6 Beyond Bohm Trajectories: Adaptive Methods
1.7 Approximations to the Quantum Force
1.8 Propagation of Derivatives Along Quantum Trajectories...
1.9 Trajectories in Phase Space
1.10 Mixed Quantum-Classical Dynamics
1.11 Additional Topics in Quantum Hydrodynamics
1.12 Quantum Trajectories for Stationary States
1.13 Coping with Problems
1.14 Topics Not Covered
1.15 Reading Guide
2 The Bohmian Route to the Hydrodynamic Equations
2.1 Introduction
2.2 The Madelung-Bohm Derivation of the Hydrodynamic Equations
2.3 The Classical Hamilton-Jacobi Equation
2.4 The Field Equations of Classical Dynamics
2.5 The Quantum Potential
2.6 The Quantum Hamilton-Jacobi Equation
2.7 Pilot 'Naves, Hidden Variables, and Bohr
3 The Phase Space Route to the Hydrodynamic Equations
3.1 Introduction
3.2 Classical Trajectories and Distribution Function in Phase Space
3.3 The Wigner Function
3.4 Moments of the Wigner Function
3.5 Equations of Motion for the Moments
3.6 Moment Analysis for Classical Phase Space Distributions
3.7 Time Evolution of Classical and Quantum Moments
3.8 Comparison Between Liouville and Hydrodynamic Phase Spaces
3.9 Discussion
4 The Dynamics and Properties of Quantum Trajectories
4.1 Introduction
4.2 Equations of Motion for the Quantum Trajectories
4.3 Wave Function Synthesis Along a Quantum Trajectory
4.4 Bohm Trajectory Integral Versus Feynman Path Integral
4.5 Wave Function Propagation and the Jacobian
4.6 The Initial Value Representation for Quantum Trajectories...
4.7 The Trajectory Noncrossing Rules
4.8 Dynamics of Quantum Trajectories Near Wave Function Nodes
4.9 Chaotic Quantum Trajectories
4.10 Examples of Chaotic Quantum Trajectories
4.11 Chaos and the Role of Nodes in the Wave Function
4.12 Why Weren't Quantum Trajectories Computed
50 Years Ago?
5 Function and Derivative Approximation on Unstructured Grids
5.1 Introduction
5.2 Least Squares Fitting Algorithms
5.3 Dynamic Least Squares
5.4 Fitting with Distributed Approximating Functionals
5.5 Derivative Computation via Tessellation and Fitting
5.6 Finite Element Method for Derivative Computation
5.7 Summary
6 Applications of the Quantum Trajectory Method Corey J. Trahan
6.1 Introduction
6.2 The Free Wave Packet
6.3 The Anisotropic Harmonic Oscillator
6.4 The Downhill Ramp Potential
6,5 Scattering from the Eckart Barrier
6.6 Discussion
7 Adaptive methods for trajectory dynamics
8 Quantum trajectories for multidimensional dynamics
9 Approximations to the quantum force
10 Derivative propagation along quantum trajectories
11 Quantum trajectories in phase space
12 Mixed quantum-classical dynamics
13 Topics in quantum hydrodynamics : the stress tensor and vorticity
14 Quantum trajectories for stationary states
15 Challenges and opportunities
Appendix. 1 Atomic units
Appendix. 2 Example QTM program
