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

1999-12  

Pengiun Group (USA)  

Gibbs, William R.  

356  

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The first half of this book is designed as a course for first year graduate students in the sciences. Problems are chosen to illustrate mathematical and physical subjects. In this first half only a moderate background in physics and mathematics is assumed. Integration, Monte Carlo techniques, the solution of linear systems and finite element methods are treated with enough depth to allow the student to understand them. An introduction to modeling with differential methods, digital signal processing and chaos is given. One chapter provides an introduction to common computer architectures.In the second half a thorough understanding of quantum mechanics is assumed with the Schrodinger equation being treated with scattering and bound state conditions. The time-dependent Schrodinger equation is also solved. A thorough introduction to the solution of the quantum-mechanical bound state with variational and Monte Carlo Green's function is given, with two examples being the solution of the bound state nuclear helium 4 and the energy of atomic liquid helium 4 at zero temperature. The exact solution of the low energy scattering problem is presented. Algorithms for the Borel and Pade methods for the summation of divergent series are studied. In the final chapter, methods for the solution of hadronic scattering from nuclei are treated including single, double and multiple scattering as well as the derivation and calculation of multiple scattering through fundamental optical models. The first half of the book will be suitable for a general course in computational methods while the second half can serve as a second semester course for Physics majors intending to do work in hadronic physics or scattering. --This text refers to an out of print or unavailable edition of this title.

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

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