Our future scientists and professionals must be conversant in computational techniques. In order to facilitate integration of computer methods into existing physics courses, this textbook offers a large number of worked examples and problems with fully guided solutions in Python as well as other languages (Mathematica, Java, C, Fortran, and Maple). It's also intended as a self-study guide for learning how to use computer methods in physics. The authors include an introductory chapter on numerical tools and indication of computational and physics difficulty level for each problem.
Author(s): Rubin H Landau; Manuel Jose Paez
Publisher: CRC Press
Year: 2018
Cover
Half Title
Title
Copyright
Contents
Acknowledgments
Series Preface
Preface
About the Authors
Web Materials
Chapter 1 Computational Basics for Physics
1.1 Chapter Overview
1.2 The Python Ecosystem
1.2.1 Python Visualization Tools
1.2.2 Python Matrix Tools
1.2.3 Python Algebraic Tools
1.3 Dealing with Floating Point Numbers
1.3.1 Uncertainties in Computed Numbers
1.4 Numerical Derivatives
1.5 Numerical Integration
1.5.1 Gaussian Quadrature
1.5.2 Monte Carlo (Mean Value) Integration
1.6 Random Number Generation
1.6.1 Tests of Random Generators
1.6.2 Central Limit Theorem
1.7 Ordinary Differential Equations Algorithms
1.7.1 Euler & Runge-Kutta Rules
1.8 Partial Differential Equations Algorithms
1.9 Code Listings
Chapter 2 Data Analytics for Physics
2.1 Chapter Overview
2.2 Root Finding
2.3 Least-Squares Fitting
2.3.1 Linear Least-Square Fitting
2.4 Discrete Fourier Transforms (DFT
2.5 Fast Fourier Transforms (FFT
2.6 Noise Reduction
2.6.1 Noise Reduction via Autocorrelation Function
2.6.2 Noise Reduction via Digital Filters
2.7 Spectral Analysis of Nonstationary Signals
2.7.1 Short-Time Fourier Transforms
2.7.2 Wavelet Analysis
2.7.3 Discrete Wavelet Transforms, Multi-Resolution Analysis
2.8 Principal Components Analysis (PCA
2.9 Fractal Dimension Determination
2.10 Code Listings
Chapter 3 Classical & Nonlinear Dynamics
3.1 Chapter Overview
3.2 Oscillators
3.2.1 First a Linear Oscillator
3.2.2 Nonlinear Oscillators
3.2.3 Assessing Precision via Energy Conservation
3.2.4 Models of Friction
3.2.5 Linear & Nonlinear Resonances
3.2.6 Famous Nonlinear Oscillators
3.2.7 Solution via Symbolic Computing
3.3 Realistic Pendula
3.3.1 Elliptic Integrals
3.3.2 Period Algorithm
3.3.3 Phase Space Orbits
3.3.4 Vibrating Pivot Pendulum
3.4 Fourier Analysis of Oscillations
3.4.1 Pendulum Bifurcations
3.4.2 Sonification
3.5 The Double Pendulum
3.6 Realistic Projectile Motion
3.6.1 Trajectory of Thrown Baton
3.7 Bound States
3.8 Three-Body Problems: Neptune, Two Suns, Stars
3.8.1 Two Fixed Suns with a Single Planet
3.8.2 Hénon-Heiles Bound States
3.9 Scattering
3.9.1 Rutherford Scattering
3.9.2 Mott Scattering
3.9.3 Chaotic Scattering
3.10 Billiards
3.11 Lagrangian and Hamiltonian Dynamics
3.11.1 Hamilton’s Principle
3.11.2 Lagrangian & Hamiltonian Problems
3.12 Weights Connected by Strings (Hard
3.13 Code Listings
Chapter 4 Wave Equations & Fluid Dynamics
4.1 Chapter Overview
4.2 String Waves
4.2.1 Extended Wave Equations
4.2.2 Computational Normal Modes
4.2.3 Masses on Vibrating String
4.2.4 Wave Equation for Large Amplitudes
4.3 Membrane Waves
4.4 Shock Waves
4.4.1 Advective Transport
4.4.2 Burgers’ Equation
4.5 Solitary Waves (Solitons
4.5.1 Including Dispersion, KdeV Solitons
4.5.2 Pendulum Chain Solitons, Sine-Gordon Solitons
4.6 Hydrodynamics
4.6.1 Navier-Stokes Equation
4.6.2 Flow over Submerged Beam
4.6.3 Vorticity Form of Navier-Stokes Equation
4.6.4 Torricelli’s Law, Orifice Flow
4.6.5 Inflow and Outflow from Square Box
4.6.6 Chaotic Convective Flow
4.7 Code Listings
Chapter 5 Electricity & Magnetism
5.1 Chapter Overview
5.2 Electric Potentials via Laplace’s & Poisson’s Equations
5.2.1 Solutions via Finite Differences
5.2.2 Laplace & Poisson Problems
5.2.3 Fourier Series vs. Finite Differences
5.2.4 Disk in Space, Polar Plots
5.2.5 Potential within Grounded Wedge
5.2.6 Charge between Parallel Planes
5.3 E&M Waves via FDTD
5.3.1 In Free Space
5.3.2 In Dielectrics
5.3.3 Circularly Polarized Waves
5.3.4 Wave Plates
5.3.5 Telegraph Line Waves
5.4 Thin Film Interference of Light
5.5 Electric Fields
5.5.1 Vector Field Calculations & Visualizations
5.5.2 Fields in Dielectrics
5.5.3 Electric Fields via Integration
5.5.4 Electric Fields via Images
5.6 Magnetic Fields via Direct Integration
5.6.1 Magnetic Field of Current Loop
5.7 Motion of Charges in Magnetic Fields
5.7.1 Mass Spectrometer
5.7.2 Quadruple Focusing
5.7.3 Magnetic Confinement
5.8 Relativity in E&M
5.8.1 Lorentz Transformations of Fields and Motion
5.8.2 Two Interacting Charges, the Breit Interaction
5.8.3 Field Propagation Effects
5.9 Code Listings
Chapter 6 Quantum Mechanics
6.1 Chapter Overview
6.2 Bound States
6.2.1 Bound States in 1-D Box (Semianalytic
6.2.2 Bound States in Arbitrary Potential (ODE Solver + Search
6.2.3 Bound States in Arbitrary Potential (Sloppy Shortcut
6.2.4 Relativistic Bound States of Klein-Gordon Equation
6.3 Spontaneous Decay Simulation
6.3.1 Fitting a Black Body Spectrum
6.4 Wave Functions
6.4.1 Harmonic Oscillator Wave Functions
6.5 Partial Wave Expansions
6.5.1 Associated Legendre Polynomials
6.6 Hydrogen Wave Functions
6.6.1 Hydrogen Radial Density
6.6.2 Hydrogen 3-D Wave Functions
6.7 Wave Packets
6.7.1 Harmonic Oscillator Wave Packets
6.7.2 Momentum Space Wave Packets
6.7.3 Solving Time-Dependent Schrödinger Equation
6.7.4 Time-Dependent Schrödinger with E Field
6.8 Scattering
6.8.1 Square Well Scattering
6.8.2 Coulomb Scattering
6.8.3 Three Disks Scattering; Quantum Chaos
6.8.4 Chaotic Quantum Billiards
6.9 Matrix Quantum Mechanics
6.9.1 Momentum Space Bound States (Integral Equations
6.9.2 k Space Bound States Delta Shell Potential
6.9.3 k Space Bound States Other Potentials
6.9.4 Hydrogen Hyperfine Structure
6.9.5 SU(3) Symmetry of Quarks
6.10 Coherent States and Entanglement
6.10.1 Glauber Coherent States
6.10.2 Neutral Kaons as Superpositions of States
6.10.3 Double Well Transitions
6.10.4 Qubits
6.11 Feynman Path Integral Quantum Mechanics
6.12 Code Listings
Chapter 7 Thermodynamics & Statistical Physics
7.1 Chapter Overview
7.2 The Heat Equation
7.2.1 Algorithm for Heat Equation
7.2.2 Solutions for Various Geometries
7.3 Random Processes
7.3.1 Random Walks
7.3.2 Diffusion-Limited Aggregation, a Fractal Walk
7.3.3 Surface Deposition
7.4 Thermal Behavior of Magnetic Materials
7.4.1 Roots of a Magnetization vs. Temperature Equation
7.4.2 Counting Spin States
7.5 Ising Model
7.5.1 Metropolis Algorithm
7.5.2 Domain Formation
7.5.3 Thermodynamic Properties
7.5.4 Extensions
7.6 Molecular Dynamics
7.6.1 16 Particles in a Box
7.7 Code Listings
Chapter 8 Biological Models: Population Dynamics & Plant Growth
8.1 Chapter Overview
8.2 The Logistic Map
8.2.1 Other Discrete and Chaotic Maps
8.3 Predator-Prey Dynamics
8.3.1 Predator-Prey Chaos
8.3.2 Including Prey Limits
8.3.3 Including Predation Efficiency
8.3.4 Two Predators, One Prey
8.4 Growth Models
8.4.1 Protein Folding as a Self-Avoiding Walk
8.4.2 Plant Growth Simulations
8.4.3 Barnsley’s Fern
8.4.4 Self-Affine Trees
8.5 Code Listings
Chapter 9 Additional Entry-Level Problems
9.1 Chapter Overview
9.2 Specular Reflection and Numerical Precision
9.3 Relativistic Rocket Golf
9.4 Stable Points in Electric Fields
9.5 Viewing Motion in Phase Space (Parametric Plots
9.6 Other Useful Visualizations
9.7 Integrating Power into Energy
9.8 Rigid-Body Rotations with Matrices
9.9 Searching for Calibration of a Spherical Tank
9.10 AC Circuits via Complex Numbers
9.10.1 Using Complex Numbers
9.10.2 RLC Circuit
9.11 Beats and Satellites
A Appendix: Python Codes
Bibliography
Index
