Computational Physics - A Practical Introduction to Computational Physics and Scientific Computing

Contents
Foreword
1 The Computer
 1.1 The Operating System
  1.1.1 Filesystem
  1.1.2 Commands
  1.1.3 Looking for Help
 1.2 Text Processing Tools – Filters
 1.3 Programming with Emacs
  1.3.1 Calling Emacs
  1.3.2 Interacting with Emacs
  1.3.3 Basic Editing
  1.3.4 Cut and Paste
  1.3.5 Windows
  1.3.6 Files and Buffers
  1.3.7 Modes
  1.3.8 Emacs Help
  1.3.9 Emacs Customization
 1.4 The Fortran Programming Language
  1.4.1 The Foundation
  1.4.2 Details
  1.4.3 Arrays
 1.5 Gnuplot
 1.6 Shell Scripting
2 Kinematics
 2.1 Motion on the Plane
  2.1.1 Plotting Data
  2.1.2 More Examples
 2.2 Motion in Space
 2.3 Trapped in a Box
  2.3.1 The One Dimensional Box
  2.3.2 Errors
  2.3.3 The Two Dimensional Box
 2.4 Applications
 2.5 Problems
3 Logistic Map
 3.1 Introduction
 3.2 Fixed Points and n 2 Cycles
 3.3 Bifurcation Diagrams
 3.4 The Newton-Raphson Method
 3.5 Calculation of the Bifurcation Points
 3.6 Liapunov Exponents
 3.7 Problems
4 Motion of a Particle
 4.1 Numerical Integration of Newton’s Equations
 4.2 Prelude: Euler Methods
 4.3 Runge–Kutta Methods
  4.3.1 A Program for the 4th Order Runge–Kutta
 4.4 Comparison of the Methods
 4.5 The Forced Damped Oscillator
 4.6 The Forced Damped Pendulum
 4.7 Appendix: On the Euler–Verlet Method
 4.8 Appendix: 2nd order Runge–Kutta Method
 4.9 Problems
5 Planar Motion
 5.1 Runge–Kutta for Planar Motion
 5.2 Projectile Motion
 5.3 Planetary Motion
 5.4 Scattering
  5.4.1 Rutherford Scattering
  5.4.2 More Scattering Potentials
 5.5 More Particles
 5.6 Problems
6 Motion in Space
 6.1 Adaptive Stepsize Control for Runge–Kutta Methods
 6.2 Motion of a Particle in an EM Field
 6.3 Relativistic Motion
 6.4 Problems
7 Electrostatics
 7.1 Electrostatic Field of Point Charges
 7.2 The Program – Appetizer and ... Desert
 7.3 The Program – Main Dish
 7.4 The Program - Conclusion
 7.5 Electrostatic Field in the Vacuum
 7.6 Results
 7.7 Poisson Equation
 7.8 Problems
8 Diffusion Equation
 8.1 Introduction
 8.2 Heat Conduction in a Thin Rod
 8.3 Discretization
 8.4 The Program
 8.5 Results
 8.6 Diffusion on the Circle
 8.7 Analysis
 8.8 Problems
9 The Anharmonic Oscillator
 9.1 Introduction
 9.2 Calculation of the Eigenvalues of Hnm (λ)
 9.3 Results
 9.4 The Double Well Potential
 9.5 Problems
10 Time Independent Schrödinger Equation
 10.1 Introduction
 10.2 The Infinite Potential Well
 10.3 Bound States
 10.4 Measurements
 10.5 The Anharmonic Oscillator - Again...
 10.6 The Lennard–Jones Potential
 10.7 Problems
11 The Random Walker
 11.1 (Pseudo)Random Numbers
 11.2 Using Pseudorandom Number Generators
 11.3 Random Walks
 11.4 Problems
12 Monte Carlo Simulations
 12.1 Statistical Physics
 12.2 Entropy
 12.3 Fluctuations
 12.4 Correlation Functions
 12.5 Sampling
  12.5.1 Simple Sampling
  12.5.2 Importance Sampling
 12.6 Markov Processes
 12.7 Detailed Balance Condition
 12.8 Problems
13 Simulation of the d = 2 Ising Model
 13.1 The Ising Model
 13.2 Metropolis
 13.3 Implementation
  13.3.1 The Program
  13.3.2 Towards a Convenient User Interface
 13.4 Thermalization
 13.5 Autocorrelations
 13.6 Statistical Errors
  13.6.1 Errors of Independent Measurements
  13.6.2 Jackknife
  13.6.3 Bootstrap
 13.7 Appendix: Autocorrelation Function
 13.8 Appendix: Error Analysis
  13.8.1 The Jackknife Method
  13.8.2 The Bootstrap Method
  13.8.3 Comparing the Methods
 13.9 Problems
14 Critical Exponents
 14.1 Critical Slowing Down
 14.2 Wolff Cluster Algorithm
 14.3 Implementation
  14.3.1 The Program
 14.4 Production
 14.5 Data Analysis
 14.6 Autocorrelation Times
 14.7 Temperature Scaling
 14.8 Finite Size Scaling
 14.9 Calculation of βc
 14.10 Studying Scaling with Collapse
 14.11 Binder Cumulant
 14.12 Appendix: Scaling
  14.12.1 Binder Cumulant
  14.12.2 Scaling
  14.12.3 Finite Size Scaling
 14.13 Appendix: Critical Exponents
  14.13.1 Definitions
  14.13.2 Hyperscaling Relations
 14.14 Problems
Bibliography
Index