现代物理学中的计算/COMPUTATION IN MODERN PHYSICS

书籍目录

Preface1 Integration  1.1 Classical Quadrature  1.2 Orthogonal Polynomials    1.2.1 Orthogonal Polynomials in the Interval -1 < x < 1    1.2.2 General Orthogonal Polynomials  1.3 Gaussian Integration    1.3.1 Geuss-Legendre Integration    1.3.2 Gaguss-Laguerre Integration  1.4 Special Integration Schemes  1.5 Principal Value Integrals2 Introduction to Monte Carlo  2.1 Preliminary Notions - - Calculating π  2.2 Evaluation of Integrals by Monte Carlo  2.3 Techniques for Direct Sampling    2.3.1 Cumulative Probability Distributions    2.3.2 The Characteristic Function φ(t)    2.3.3 The Fundamental Theorem of Sampling    2.3.4 Sampling Monomials 0 < z < 1    2.3.5 Sampling Functions 0 < x < ∞    2.3.6 Brute-force Inversion of F(x)    2.3.7 The Rejection Technique    2.3.8 Sums of Random Variables    2.3.9 Selection on the Random Variables    2.3.10 The Sum of Probability Distribution Functions  2.4 The Metropolis Algorithm    2.4.1 The Method Itself    2.4.2 Why It Works    2.4.3 Comments on the Algorithm3 Differential Methods  3.1 Difference Schemes    3.1.1 Elementary Considerations    3.1.2 The General Case  3.2 Simple Differential Equations  3.3 Modeling with Differential Equations4 Computers for Physicists  4.1 Fundamentals    4.1.1 Representation of Negative Numbers    4.1.2 Logical Operations    4.1.3 Integer Formats    4.1.4 Floating Point Formats  4.2 The i8086 Series    4.2.1 The Stack    4.2.2 Memory Addressing    4.2.3 Internal Registers of the CPU    4.2.4 Instructions    4.2.5 Sample Program    4.2.6 The Floating Point Co-processor i8087  4.3 Cray-1 S Architecture    4.3.1 Vector Operations and Chaining    4.3.2 Coding for Maximum Speed  4.4 Intel i860 Architecture5 Linear Algebra  5.1 X2 Analysis  5.2 Solution of Linear Equations    5.2.1 LU Reductions    5.2.2 The Gauss-Seidel Method    5.2.3 The Householder Transformation  5.3 The Eigenvalue Problem    5.3.1 Coupled Oscillators    5.3.2 Finding the Eigenvalues of a Matrix    5.3.3 Tridiagonal Symmetric Matrices    5.3.4 The Role of Orthogonal Matrices    5.3.5 The Householder Method    5.3.6 The Lanczos Algorithm6 Exercises in Monte Carlo7 Finite Element Methods8 Digital Signal Processing9 Chaos10 The Schrodinger Equation11 The N-body Ground State12 Divergent Series13 Scattering in the N-body SystemA ProgramsIndex

作者简介

The use of computers to solve modern scientific problems is very widespread. The impact of the improvement of our techniques for the solution of complex problems is difficult to overstate. Even our approach to most problems has been changed. Solutions to problems once thought intractable are being routinely secured. Instead of using oversimplified models, as has been the practice for the treatment of scientific systems in the past, the entire problem can now be attacked.The second edition of Computation in Modern Physics develops and presents algorithms for the solution of many types of mathematical systems, some dating as far as the last few centuries, but also quite a number that have been developed within the last 10-50 years.In this last category, close attention is paid to the rapidly developing area of Monte Carlo techniques where new conceptual views of physics problems are being brought into play. With this method, problems in a large number of dimensions can be solved through the introduction of a modern method for the representation of multidimensional functions.This book is suitable for two different levels in computational physics. The first part is an advanced introductory level and is appropriate for good students with no previous experience in computational methods or any student with some experience. Here the student is introduced to integral and differential techniques, Monte Carlo integration, basic computer architecture, methods of linear algebra, finite element techniques, digital signal processing and chaos.The second part of the book is more specialized for problems in strong interaction with emphasis on solutions to many-body scattering problems andseveral-body bound state calculations with Monte Carlo techniques. It also contains a chapter dealing with techniques for the summation of divergent series.

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