Numerical Quantum Dynamics

It is an indisputable fact that computational physics form part of the essential landscape of physical science and physical education. When writing such a book, one is faced with numerous decisions, e. g. : Which topics should be included? What should be assumed about the readers' prior knowledge? How should balance be achieved between numerical theory and physical application? This book is not elementary. The reader should have a background in qu- tum physics and computing. On the other way the topics discussed are not addressed to the specialist. This work bridges hopefully the gap between - vanced students, graduates and researchers looking for computational ideas beyond their fence and the specialist working on a special topic. Many imp- tant topics and applications are not considered in this book. The selection is of course a personal one and by no way exhaustive and the material presented obviously reflects my own interest. What is Computational Physics? During the past two decades computational physics became the third fun- mental physical discipline. Like the 'traditional partners' experimental physics and theoretical physics, computational physics is not restricted to a special area, e. g. , atomic physics or solid state physics. Computational physics is a meth- ical ansatz useful in all subareas and not necessarily restricted to physics. Of course this methods are related to computational aspects, which means nume- cal and algebraic methods, but also the interpretation and visualization of huge amounts of data.

Contenu

List of Figures. List of Tables. Preface. 1: Introduction to Quantum Dynamics. 1. The Schrödinger Equation. 2. Dirac Description of Quantum States. 3. Angular Momentum. 4. The Motion of Wave Packets. 5. The Quantum-Classical Correspondence. 2: Separability. 1. Classical and Quantum Integrability. 2. Separability in Three Dimensions. 3. Coordinates and Singularities. 3: Approximation by Perturbation Techniques. 1. The Rayleigh-Schrödinger Perturbation Theory. 2. 1/N-Shift Expansions. 3. Approximative Symmetry. 4. Time-Dependent Perturbation Theory. 4: Approximation Techniques. 1. The Variational Principle. 2. The Hartree-Fock Method. 3. Density Functional Theory. 4. The Virial Theorem. 5. Quantum Monte Carlo Methods. 5: Finite Differences. 1. Initial Value Problems for Ordinary Differential Equations. 2. The Runge-Kutta Method. 3. Predictor-Corrector Methods. 4. Finite Differences in Space and Time. 5. The Numerov Method. 6: Discrete Variable Method. 1. Basic Idea. 2. Theory. 3. Orthogonal Polynomials and Special Functions. 4. Examples. 5. The Laguerre Mesh. 7: Finite Elements. 1. Introduction. 2. Unidimensional Finite Elements. 3. Adaptive Methods: Some Remarks. 4. B-Splines. 5. Two-Dimensional Finite Elements.6. Using Different Numerical Techniques in Combination. 8: Software Sources. Acknowledgments. Index.