Computational Physics

, by Landau, Rubin H.; Mejia, Manuel J. Paez; Kowallik, Hans; Jansen, Heri

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780471115908 | 0471115908
Cover: Hardcover
Copyright: 5/1/1997

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With this engaging book as a guide, advanced undergraduates and first-year graduate students will gain confidence in their abilities and develop new insight into the physical sciences as they use their computers to address challenging and stimulating problems.

Preface

xxi

(4)

Acknowledgments

xxv

(2)

Acronyms

xxvii

Part I GENERALITIES

(60)

1 Introduction

(6)

1.1 The Nature of Computational Science

(2)

1.1.1 How Computational Scientists Do It

(1)

1.2 Aims of This Book

(1)

1.3 Using this Book with the Disk and Web

(3)

2 Computing Software Basics

(22)

2.1 Problem 1: Making Computers Obey

(1)

2.2 Theory: Computer Languages

(2)

2.3 Implementation: Programming Concepts

(1)

2.4 Implementation: Fortran, area. f

(1)

2.5 Implementation: C, area. c

(1)

2.6 Implementation: Shells, Editors, and Programs

(1)

2.7 Theory: Program Design

(2)

2.8 Method: Structured Programming

(2)

2.9 Method: Programming Hints

(2)

2.10 Problem 2: Limited Range of Numbers

(1)

2.11 Theory: Number Representation

(1)

2.12 Method: Fixed and Floating

(2)

2.13 Implementation: Over/Underflows, over. f (.c)

(1)

2.14 Model: Machine Precision

(2)

2.15 Implementation: limit.f (.c)

(1)

2.16 Problem 3: Complex Numbers, Inverse Functions

(1)

2.17 Theory: Complex Numbers

(2)

2.18 Implementation: complex.c (.f)

(1)

2.19 Exploration: Quantum Complex Energies

(1)

2.20 Problem 4: Summing Series

(1)

2.21 Method: Numeric

(1)

2.22 Implementation: Pseudocode

(1)

2.23 Implementation: Good Algorithm, exp-good.f (.c)

(1)

2.24 Implementation: Bad Algorithm, exp-bad.f(.c)

(1)

2.25 Assessment

(1)

3 Errors and Uncertainties in Computations

(16)

3.1 Problem: Living with Errors

(1)

3.2 Theory: Types of Errors

(1)

3.3 Model: Subtactive Concellation

(1)

3.4 Assessment: Cancellation: Experiment

(2)

3.5 Model: Multiplicative Error

(1)

3.6 Problem 1: Errors in Spherical Bessel Functions

(1)

3.7 Method: Numeric Recursion Relations

(2)

3.8 Implementation: bessel.F (.c)

(1)

3.9 Assessment

(1)

3.10 Problem 2: Error in Algorithms

(1)

3.11 Model: Errors in Algorithms

(1)

3.11.1 Total Error

(1)

3.12 Method: Optimizing with Known Error Behavior

(1)

3.13 Method: Empirical Error Analysis

(1)

3.14 Assessment: Experiment

(3)

4 Integration

(16)

4.1 Problem: Integrating a Spectrum

(1)

4.2 Model: Quadrature, Summing Boxes

(3)

4.3 Method: Trapezoid Rule

(1)

4.4 Method: Simpson's Rule

(1)

4.5 Assessment: Integration Error, Analytic

(3)

4.6 Method: Gaussian Quadrature

(3)

4.6.1 Scaling Integration Points

(2)

4.7 Implementation: integ.f (.c)

(1)

4.8 Assessment: Empirical Error Estimate

(1)

4.9 Assessment: Experimentation

(1)

4.10 Method: Romberg Extrapolation

(4)

4.10.1 Other Closed Newton-Cotes Formulas

(3)

Part II APPLICATIONS

(280)

5 Data Fitting

(20)

5.1 Problem: Fitting an Experimental Spectrum

(1)

5.2 Theory: Curve Fitting

(1)

5.3 Method: Lagrange Interpolation

(2)

5.3.1 Example

(1)

5.4 Implementation: lagrange.f (.c)

(1)

5.5 Assessment: Interpolating a Resonant Spectrum

(1)

5.6 Assessment: Exploration

(1)

5.7 Method: Cubic Splines

(2)

5.7.1 Cubic Spline Boundary Conditions

(1)

5.7.2 Exploration: Cubic Spline Quadrature

(1)

5.8 Implementation: Spline.f

(1)

5.9 Assessment: Spline Fit of Cross Section

(1)

5.10 Problem: Fitting Exponential Decay

(1)

5.11 Model: Exponential Decay

(1)

5.12 Theory: Probability Theory

(2)

5.13 Method: Least-Squares Fitting

(2)

5.14 Theory: Goodness of Fit

(1)

5.15 Implementation: Least-Squares Fits, fit.f (.c)

(1)

5.16 Assessment: Fitting Exponential Decay

(1)

5.17 Assessment: Fitting Heat Flow

(1)

5.18 Implementation: Linear Quadratic Fits

(1)

5.19 Assessment: Quadratic Fit

(1)

5.20 Method: Nonlinear Least-Squares Fitting

(1)

5.21 Assessment: Nonlinear Fitting

(1)

6 Deterministic Randomness

(10)

6.1 Problem: Deterministic Randomness

(1)

6.2 Theory: Random Sequences

(1)

6.3 Method: Pseudo-Random-Number Generators

(2)

6.4 Assessment: Random Sequences

(1)

6.5 Implementation: Simple and Not random.f (.c); call.f (.c)

(1)

6.6 Assessment: Randomness and Uniformity

(1)

6.7 Assessment: Tests of Randomness, Uniformity

(1)

6.8 Problem: A Random Walk

(1)

6.9 Model: Random Walk Simulation

(1)

6.10 Method: Numerical Random Walk

(1)

6.11 Implementation: walk.f (.c)

(1)

6.12 Assessment: Different Random Walkers

(2)

7 Monte Carlo Applications

(16)

7.1 Problem: Radioactive Decay

(1)

7.2 Theory: Spontaneous Decay

(1)

7.3 Model: Discrete Decay

(1)

7.4 Model: Continuous Decay

(1)

7.5 Method: Decay Simulation

(2)

7.6 Implementation: decay.f (.c)

(1)

7.7 Assessment: Decay Visualization

(1)

7.8 Problem: Measuring by Stone Throwing

(1)

7.9 Theory: Integration by Rejection

(2)

7.10 Implementation: Stone Throwing, pond.f (.c)

(1)

7.11 Problem: High-Dimensional Integration

(1)

7.12 Method: Integration by Mean Value

100

(1)

7.12.1 Multidimensional Monte Carlo

101

(1)

7.13 Assessment: Error in N-D Integration

101

(1)

7.14 Implementation: 10-D Integration, int_10d.f (.c)

102

(1)

7.15 Problem: Integrate a Rapidly Varying Function.

102

(1)

7.16 Method: Variance Reduction.

102

(1)

7.17 Method: Importance Sampling.

103

(1)

7.18 Implementation: Nonuniform Randomness.

103

(4)

7.18.1 Inverse Transform Method

104

(1)

7.18.2 Uniform Weight Function w

105

(1)

7.18.3 Exponential Weight

105

(1)

7.18.4 Gaussian (Normal) Distribution

106

(1)

7.18.5 Alternate Gaussian Distribution

107

(1)

7.19 Method: von Neumann Rejection.

107

(1)

7.20 Assessment.

108

(1)

8 Differentiation

109

(8)

8.1 Problem 1: Numerical Limits

109

(1)

8.2 Method: Numeric

109

(3)

8.2.1 Method: Forward Difference

109

(2)

8.2.2 Method: Central Difference

111

(1)

8.2.3 Method: Extrapolated Difference

111

(1)

8.3 Assessment: Error Analysis

112

(2)

8.4 Implementation: Differentiation, diff.f (.c)

114

(1)

8.5 Assessment: Error Analysis, Numerical

114

(1)

8.6 Problem 2: Second Derivatives

114

(1)

8.7 Theory: Newton II

114

(1)

8.8 Method: Numerical Second Derivatives

114

(1)

8.9 Assessment: Numerical Second Derivatives

115

(2)

9 Differential Equations and Oscillations

117

(14)

9.1 Problem: A Forced Nonlinear Oscillator

117

(1)

9.2 Theory, Physics: Newton's Laws

117

(1)

9.3 Model: Nonlinear Oscillator

118

(1)

9.4 Theory, Math: Types of Equations

119

(3)

9.4.1 Order

119

(1)

9.4.2 Ordinary and Partial

120

(1)

9.4.3 Linear and Nonlinear

121

(1)

9.4.4 Initial and Boundary Conditions

121

(1)

9.5 Theory, Math, and Physics: The Dynamical Form for ODEs

122

(1)

9.5.1 Second-Order Equation

122

(1)

9.6 Implementation: Dynamical Form for Oscillator

123

(1)

9.7 Numerical Method: ODE Algorithms

124

(1)

9.8 Method (Numerical): Euler's Algorithm

125

(1)

9.9 Method (Numerical): Second-Order Runge-Kutta

126

(1)

9.10 Method (Numerical): Fourth-Order Runge-Kutta

127

(1)

9.11 Implementation: ODE Solver, rk4.f (.c)

128

(1)

9.12 Assessment: rk4 and Linear Oscillations

128

(1)

9.13 Assessment: rk4 and Nonlinear Oscillations

129

(1)

9.14 Exploration: Energy Conservation

129

(2)

10 Quantum Eigenvalues; Zero-Finding and Matching

131

(12)

10.1 Problem: Binding A Quantum Particle

131

(1)

10.2 Theory: Quantum Waves

132

(1)

10.3 Model: Particle in a Box

133

(1)

10.4 Solution: Semianalytic

133

(3)

10.5 Method: Finding Zero via Bisection Algorithm

136

(1)

10.6 Method: Eigenvalues from an ODE Solver

136

(4)

10.6.1 Matching

139

(1)

10.7 Implementation: ODE Eigenvalues, numerov.c

140

(1)

10.8 Assessment: Explorations

141

(1)

10.9 Extension: Newton's Rule for Finding Roots

142

(1)

11 Anharmonic Oscillations

143

(8)

11.1 Problem 1: Perturbed Harmonic Oscillator

143

(1)

11.2 Theory: Newton II

144

(1)

11.3 Implementation: ODE Solver, rk4.f (.c)

144

(1)

11.4 Assessment: Amplitude Dependence of Frequency

145

(1)

11.5 Problem 2: Realistic Pendulum

145

(1)

11.6 Theory: Newton II for Rotations

146

(1)

11.7 Method, Analytic: Elliptic Integrals

147

(1)

11.8 Implementation, rk4 for Pendulum

147

(1)

11.9 Exploration: Resonance and Beats

148

(1)

11.10 Exploration: Phases-Space Plot

149

(1)

11.11 Exploration: Damped Oscillator

150

(1)

12 Fourier Analysis of Nonlinear Oscillations

151

(20)

12.1 Problem 1: Harmonics in Nonlinear Oscillations

151

(1)

12.2 Theory: Fourier Analysis

152

(3)

12.2.1 Example 1: Sawtooth Function

154

(1)

12.2.2 Example 2: Half-Wave Function

154

(1)

12.3 Assessment: Summation of Fourier Series

155

(1)

12.4 Theory: Fourier Transforms

156

(1)

12.5 Method: Discrete Fourier Transform

157

(4)

12.6 Method: DFT for Fourier Series

161

(1)

12.7 Implementation: fourier.f (.c), invfour.c

162

(1)

12.8 Assessment: Simple Analytic Input

162

(1)

12.9 Assessment: Highly Nonlinear Oscillator

163

(1)

12.10 Assessment: Nonlinearly Perturbed Oscillator

163

(1)

12.11 Exploration: DFT of Nonperiodic Functions

164

(1)

12.12 Exploration: Processing Noisy Signals

164

(1)

12.13 Model: Autocorrelation Function

164

(2)

12.14 Assessment: DFT and Autocorrelation Function

166

(1)

12.15 Problem 2: Model Dependence of Data Analysis.

167

(1)

12.16 Method: Model-Independent Data Analysis

167

(2)

12.17 Assessment

169

(2)

13 Unusual Dynamics of Nonlinear Systems

171

(10)

13.1 Problem: Variability of Bug Populations

171

(1)

13.2 Theory: Nonlinear Dynamics

171

(1)

13.3 Model: Nonlinear Growth, The Logistic Map

172

(2)

13.3.1 The Logistic Map

173

(1)

13.4 Theory: Properties of Nonlinear Maps

174

(2)

13.4.1 Fixed Points

174

(1)

13.4.2 Period Doubling, Attractors

175

(1)

13.5 Implementation: Explicit Mapping

176

(1)

13.6 Assessment: Bifurcation Diagram

177

(1)

13.7 Implementation: bugs.f (.c)

178

(1)

13.8 Exploration: Random Numbers via Logistic Map

179

(1)

13.9 Exploration: Feigenbaum Constants

179

(1)

13.10 Exploration: Other Maps

180

(1)

14 Differential Chaos in Phase Space

181

(16)

14.1 Problem: A Pendulum Becomes Chaotic

181

(1)

14.2 Theory and Model: The Chaotic Pendulum

182

(1)

14.3 Theory: Limit Cycles and Mode Locking

183

(1)

14.4 Implementation 1: Solve ODE, rk4.f (.c)

184

(1)

14.5 Visualization: Phase-Space Orbits

184

(3)

14.6 Implementation 2: Free Oscillations

187

(1)

14.7 Theory: Motion in Phase Space

188

(1)

14.8 Implementation 3: Chaotic Pendulum

188

(3)

14.9 Assessment: Chaotic Structure in Phase Space

191

(1)

14.10 Assessment: Fourier Analysis

191

(1)

14.11 Exploration: Pendulum with Vibrating Pivot

192

(2)

14.11.1 Implemention: Bifurcation Diagram

193

(1)

14.12 Further Explorations

194

(3)

15 Matrix Computing and Subroutine Libraries

197

(34)

15.1 Problem 1: Many Simultaneous Linear Equations

197

(1)

15.2 Formulation: Linear into Matrix Equation

198

(1)

15.3 Problem 2: Simple but Unsolvable Statics

198

(1)

15.4 Theory, Statics

199

(1)

15.5 Formulation: Nonlinear Simultaneous Equations

200

(1)

15.6 Theory: Matrix Problems

201

(3)

15.6.1 Classes of Matrix Problems

201

(3)

15.7 Methof: Matrix Computing

204

(3)

15.8 Implementation: Scientific Libraries, WWW

207

(2)

15.9 Implementation: Determining Availability

209

(5)

15.9.1 Determining Contents of a Library

210

(1)

15.9.2 Determining the Needed Routine

210

(1)

15.9.3 Calling LAPACK from Fortran, lineq.c

211

(1)

15.9.4 Calling LAPACK from C

212

(1)

15.9.5 Calling LAPACK Fortran from C

213

(1)

15.9.6 C Compiling Calling Fortran

214

(1)

15.10 Extension: More Netlib Libraries

214

(2)

15.10.1 SLATEC's Common Math Library

215

(1)

15.11 Exercises: Testing Matrix Calls

216

(2)

15.12 Implementation: LAPACK Short Contents

218

(3)

15.13 Implementation: Netlib Short Contents

221

(1)

15.14 Implementation: SLATEC Short Contents

222

(9)

16 Bound States in Momentum Space

231

(8)

16.1 Problem: Bound States in Nonlocal Potentials

231

(1)

16.2 Theory: k-Space Schrodinger Equation

232

(1)

16.3 Method: Reducing Integral to Linear Equations

233

(2)

16.4 Model: The Delta-Shell Potential

235

(1)

16.5 Implementation: Binding Energies, bound.c (.f)

236

(1)

16.6 Exploration: Wave Function

237

(2)

17 Quantum Scattering via Integral Equations.

239

(10)

17.1 Problem: Quantum Scattering in k Space

239

(1)

17.2 Theory, Lippmann-Schwinger Equation

240

(1)

17.3 Theory, Mathematics: Singular Integrals

241

(2)

17.3.1 Numerical Principal Values

242

(1)

17.4 Method: Converting Integral to Matrix Equations

243

(3)

17.4.1 Solution via Inversion or Elimination

245

(1)

17.4.2 Solving ie Integral Equations.

245

(1)

17.5 Implementation: Delta-Shell Potential, scatt.f

246

(2)

17.6 Exploration: Scattering Wave Function

248

(1)

18 Computing Hardware Basics: Memory and CPU

249

(14)

18.1 Problem: Speeding Up Your Program

249

(1)

18.2 Theory: High-Performance Components

250

(6)

18.2.1 Memory Hierarchy

250

(4)

18.2.2 The Central Processing Unit

254

(1)

18.2.3 CPU Design: RISC

254

(1)

18.2.4 CPU Design: Vector Processing

255

(1)

18.2.5 Virtual Memory

256

(1)

18.3 Method: Programming for Virtual Memory

256

(1)

18.4 Implementation: Good, Bad Virtual Memory Use

257

(1)

18.5 Method: Programming for Data Cache

258

(2)

18.6 Implementation 1: Cache Misses

260

(1)

18.7 Implementation 2: Cache Misses

260

(1)

18.8 Implementation 3: Large Matrix Multiplication

261

(2)

19 High-Performance Computing: Profiling and Tuning

263

(12)

19.1 Problem: Effect of Hardware on Performance

263

(1)

19.2 Method: Tabulating Speedups

263

(1)

19.3 Implementation 1: Baseline Program, tune.f

264

(1)

19.4 Method: Profiling

265

(1)

19.5 Implementation 2: Basic Optimization, tune1.f

266

(3)

19.6 Implementation 2: Vector Tuning, tune2.f

269

(1)

19.7 Implementation 3: Vector Code on RISC, tune3.f

270

(1)

19.8 Implementation 4: Superscalar Tuning, tune4.f

271

(2)

19.9 Assessment

273

(2)

20 Parallel Computing and PVM

275

(8)

20.1 Problem: Speeding Up Your Program

275

(1)

20.2 Theory: Parallel Semantics

276

(2)

20.2.1 Parallel Instruction and Data Streams

276

(1)

20.2.2 Granularity

277

(1)

20.2.3 Parallel Performance

277

(1)

20.3 Method: Multitasking Programming

278

(1)

20.3.1 Method: Multitask Organization

278

(1)

20.4 Method: Distributed Memory Programming

279

(1)

20.5 Implementation: PVM Bug Populations, WWW

280

(3)

20.5.1 The Plan

280

(3)

21 Object-Oriented Programming: Kinematics.

283

(14)

21.1 Problem: Superposition of Motions

283

(1)

21.2 Theory: Object-Oriented Programming

284

(1)

21.2.1 OOP Fundamentals

284

(1)

21.3 Theory: Newton's Laws, Equation of Motion

285

(1)

21.4 OOP Method: Class Structure

285

(1)

21.5 Implementation: Uniform 1-D Motion, unim1d.cpp

286

(9)

21.5.1 Uniform Motion in 1-D, Class Um1D

287

(1)

21.5.2 Implementation: Uniform Motion in 2-D, Child Um2D, unimot2d.cpp

288

(1)

21.5.3 Class Um2D: Uniform Motion in 2-D

289

(2)

21.5.4 Implementation: Projectile Motion, Child Accm2D, accm2d.cpp

291

(2)

21.5.5 Accelerated Motion in Two Directions

293

(2)

21.6 Assessment: Exploration, shms.cpp

295

(2)

22 Thermodynamic Simulations: The Ising Model

297

(12)

22.1 Problem: Hot Magnets

297

(1)

22.2 Theory: Statistical Mechanics

297

(2)

22.3 Model: An Ising Chain

299

(2)

22.4 Solution, Analytic

301

(1)

22.5 Solution, Numerical: The Metropolis Algorithm

301

(3)

22.6 Implementation: ising.f (.c)

304

(1)

22.7 Assessment: Approach to Thermal Equilibrium

305

(1)

22.8 Assessment: Thermodynamic Properties

305

(2)

22.9 Exploration: Beyond Nearest Neighbors

307

(1)

22.10 Exploration: 2-D and 3-D Ising Models

307

(2)

23 Functional Integration on Quantum Paths.

309

(14)

23.1 Problem: Relate Quantum to Classical Trajectory

309

(1)

23.2 Theory: Feynman's Spacetime Propagation

309

(3)

23.3 Analytic Method: Bound-State Wave Function

312

(2)

23.4 Numerical Method: Lattice Path Integration

314

(2)

23.5 Method: Lattice Computation of Propagators

316

(3)

23.6 Implementation: qmc.f (.c)

319

(2)

23.7 Assessment and Exploration

321

(2)

24 Fractals

323

(20)

24.1 Problem: Fractals

323

(1)

24.2 Theory: Fractional Dimension

324

(11)

24.3 Problem 1: The Sierrpinski Gasket

324

(1)

24.4 Implementation: sierpin.c

325

(1)

24.5 Assessment: Determining a Fractal Dimension

326

(1)

24.6 Problem 2: How to Grow Beautiful Plants

327

(1)

24.7 Theory: Self-Affine Connections

328

(1)

24.8 Implementation: Barnsley's Fern, fern.c

329

(1)

24.9 Exploration: Self-Affinity in Trees

330

(1)

24.10 Implementation: Nice Trees, tree.c

330

(1)

24.11 Problem 3: Ballistic Deposition

330

(1)

24.12 Method

331

(2)

24.13 Implementation: Ballistic Deposition, film.c

333

(1)

24.14 Problem 4: Length of the Coastline of Britain

333

(1)

24.15 Model: The Coast as a Fractal

333

(1)

24.16 Method: Box Counting

334

(1)

24.17 Problem 5: Correlated Growth, Forests and Films

335

(1)

24.18 Method: Correlated Ballistic Deposition

336

(1)

24.19 Implementation: column.c

337

(1)

24.20 Problem 6: A Globular Cluster

337

(1)

24.21 Model: Diffusion-Limited Aggregation

337

(1)

24.22 Method: DLA Simulation

338

(1)

24.23 Implementation: dla.c

339

(1)

24.24 Assessment: Fractal Analysis of DLA Graph

339

(1)

24.25 Problem 7: Fractals in Bifurcation Graph

340

(3)

Part III PARTIAL DIFFERENTIAL EQUATIONS

343

(36)

25 Electrostatic Potentials

343

(12)

25.1 Introduction: Types of PDE'S

343

(1)

25.2 Problem: Determining an Electrostatic Potential

344

(1)

25.3 Theory: Laplace's Equation (Elliptic PDE)

344

(1)

25.4 Method, Numerical: Finite Difference

345

(2)

25.5 Method, Analytic: Polynomial Expansions

347

(3)

25.6 Implementation: Solution on Lattice, laplace.f

350

(1)

25.7 Assessment and Visualization

351

(1)

25.8 Exploration

351

(1)

25.9 Exploration: Parallel-Plate Capacitor

352

(1)

25.10 Exploration: Field Between Square Conductors

352

(3)

26 Heat Flow

355

(10)

26.1 Problem: Heat Flow in a Metal Bar

355

(1)

26.2 Model: The Heat (Parabolic) PDE

355

(1)

26.3 Method, Analytic: Polynomial Expansions

356

(2)

26.4 Method, Numerical: Finite Difference

358

(1)

26.5 Analytic Assessment: Algorithm

359

(1)

26.6 Implementation, Heat Equation, eqheat.f (.c)

360

(1)

26.7 Assessment: Continuity, Numeric vs Analytic

361

(1)

26.8 Assessment: Visualization

362

(1)

26.9 Exploration

362

(3)

27 Waves on a String

365

(14)

27.1 Problem: A Vibrating String

365

(1)

27.2 Model: The Wave Equation (Hyperbolic PDE)

365

(2)

27.3 Method, Numerical: Time Stepping

367

(2)

27.4 Method, Analytic: Normal Modes

369

(2)

27.5 Implementation: eqstring.f (.c)

371

(1)

27.6 Assessment: Visualization

371

(1)

27.7 Exploration

372

(1)

Part IV NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

379

(30)

28 Solitons, the Kde V Equation.

379

(10)

28.1 Introduction

379

(1)

28.2 Problem: Solitons

380

(1)

28.3 Theory: The Korteweg-de Vries Equation

381

(3)

28.4 Method, Analytic

384

(1)

28.5 Method, Numeric: Finite Difference

384

(2)

28.6 Implementation: Kde V Solitons, soliton.f (.c)

386

(1)

28.7 Assessment: Visualization

387

(1)

28.8 Exploration: Two Solitons Crossing

387

(1)

28.9 Exploration: Phase-Space Behavior

388

(1)

28.10 Exploration: ShockWaves

388

(1)

29 Sine-Gordon Solitons

389

(10)

29.1 Problem 1: Particles from field Equations

389

(1)

29.2 Theory: Circular Ring Solitons (Pulsons)

389

(1)

29.3 Problem 2: Dispersionless Dispersive Chains

390

(1)

29.4 Theory: Coupled Pendula

390

(2)

29.4.1 Dispersion in Linear Chain

392

(1)

29.4.2 Continuum Limit, the SGE

393

(1)

29.5 Solution: Analytic

394

(1)

29.6 Solution: Numeric

395

(2)

29.7 Implementation, 2-D Solitons, twodsol.f (.c)

397

(1)

29.8 Visualization

398

(1)

30 Confined Electronic Wave Packets.

399

(10)

30.1 Problem: A Confined Electron

399

(1)

30.2 Model: Time-Dependent Schrodinger Equation

399

(2)

30.3 Method, Numeric: Finite Difference

401

(2)

30.4 Implementation: Wave Packet in Well, sqwell.f

403

(1)

30.5 Assessment: Visualization, and Animation

403

(1)

30.6 Exploration: 1-D Harmonic Oscillator

404

(1)

30.7 Implementation: harmos.f

404

(1)

30.8 Problem: Two-Dimensional Confinement

404

(2)

30.9 Method: Numerical

406

(1)

30.10 Exploration: 2-D Harmonic Oscillator

407

(1)

30.11 Exploration: Single-Slit Diffraction, slit.f

408

(1)

Appendix A: Analogous Elements in Fortran and C

409

(2)

Appendix B: Programs on Floppy Diskette

411

(6)

Appendix C: Listing of C Programs

417

(44)

Appendix D: Listing of Fortran Programs

461

(40)

Appendix E: Typical Project Assignments

501

(2)

E.1 First Quarter (10 weeks)

501

(1)

E.2 Second Quarter (10 weeks)

502

(1)

Glossary

503

(6)

References

509

(6)

Index

515

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Computational Physics

Summary

Author Biography

Table of Contents

Supplemental Materials