Numerical Quantum Dynamics by W. SchweizerNumerical Quantum Dynamics by W. Schweizer

Numerical Quantum Dynamics

byW. Schweizer

Paperback | October 28, 2010

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This book describes computational methods used in quantum dynamics with emphasis on small quantum systems. Computational physics is a fundamental physical discipline at the forefront of physical research. Thus it is an indisputable fact that computational physics form part of the essential landscape of physical science and education. In the present state of scientific knowledge the importance of quantum dynamics is commonplace. Computational quantum dynamics involves the use of computer calculations and simulations to solve quantum physical problems. Following a brief introduction to quantum dynamics the book revisits approximation techniques based on perturbational theory and variationalmethods. This discussion includes Hartree-Fock and density functional theory and quantum Monte Carlo methods. The next chapter presents the concepts of finite differences. Central in this chapter is the discretization in time and space. Later chapters concentrate on discrete variable techniques based on orthogonal polynomials, finite element and B-splinemethods for both time-independent and time-dependent problems and the combination of different computational techniques. The final chapter contains a list of useful sources for computational software and program codes. This book is primarily aimed at advanced students and graduates and researchers in theoretical and computational physics or chemistry and bridges the gap between quantum textbooks and computational research. Although not essential, the reader should have a basic background in quantum physics and some knowledge of numerical analysis would be helpful in reading this book.
Title:Numerical Quantum DynamicsFormat:PaperbackDimensions:286 pages, 9.25 × 6.1 × 0.68 inPublished:October 28, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048159148

ISBN - 13:9789048159147

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Table of Contents

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.