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9780471115908

Computational Physics

by ; ; ;
  • ISBN13:

    9780471115908

  • ISBN10:

    0471115908

  • Edition: Disk
  • Format: Hardcover
  • Copyright: 1997-05-01
  • Publisher: Wiley-Interscience

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Summary

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.

Author Biography

Rubin H. Landau, Phd, is a professor in the Department of Physics at Oregon State University in Corvallis. He teaches the course in computational physics, helps direct the Northwest Alliance for Computational Science and Engineering, and has been using computers in theoretical physics research for the past 30 years. The author of more than 70 refereed publications, he is the author of Quantum Mechanics II and A Scientist's and Engineer's Guide to Workstations and Supercomputers, both available from Wiley.<br> <br> J. Pßez, PhD, is a professor in the Department of Physics at the University of Antioquia in Medellfn, Colombia. He teaches courses in computational physics, programming, and nuclear physics. He and Professor Landau have conducted pioneering computational investigations in the interactions of mesons and nucleons with nuclei.

Table of Contents

Preface xxi(4)
Acknowledgments xxv(2)
Acronyms xxvii
Part I GENERALITIES 3(60)
1 Introduction
3(6)
1.1 The Nature of Computational Science
3(2)
1.1.1 How Computational Scientists Do It
4(1)
1.2 Aims of This Book
5(1)
1.3 Using this Book with the Disk and Web
6(3)
2 Computing Software Basics
9(22)
2.1 Problem 1: Making Computers Obey
9(1)
2.2 Theory: Computer Languages
9(2)
2.3 Implementation: Programming Concepts
11(1)
2.4 Implementation: Fortran, area. f
12(1)
2.5 Implementation: C, area. c
13(1)
2.6 Implementation: Shells, Editors, and Programs
13(1)
2.7 Theory: Program Design
14(2)
2.8 Method: Structured Programming
16(2)
2.9 Method: Programming Hints
18(2)
2.10 Problem 2: Limited Range of Numbers
20(1)
2.11 Theory: Number Representation
20(1)
2.12 Method: Fixed and Floating
21(2)
2.13 Implementation: Over/Underflows, over. f (.c)
23(1)
2.14 Model: Machine Precision
23(2)
2.15 Implementation: limit.f (.c)
25(1)
2.16 Problem 3: Complex Numbers, Inverse Functions
25(1)
2.17 Theory: Complex Numbers
25(2)
2.18 Implementation: complex.c (.f)
27(1)
2.19 Exploration: Quantum Complex Energies
28(1)
2.20 Problem 4: Summing Series
29(1)
2.21 Method: Numeric
29(1)
2.22 Implementation: Pseudocode
29(1)
2.23 Implementation: Good Algorithm, exp-good.f (.c)
30(1)
2.24 Implementation: Bad Algorithm, exp-bad.f(.c)
30(1)
2.25 Assessment
30(1)
3 Errors and Uncertainties in Computations
31(16)
3.1 Problem: Living with Errors
31(1)
3.2 Theory: Types of Errors
32(1)
3.3 Model: Subtactive Concellation
33(1)
3.4 Assessment: Cancellation: Experiment
34(2)
3.5 Model: Multiplicative Error
36(1)
3.6 Problem 1: Errors in Spherical Bessel Functions
37(1)
3.7 Method: Numeric Recursion Relations
38(2)
3.8 Implementation: bessel.F (.c)
40(1)
3.9 Assessment
40(1)
3.10 Problem 2: Error in Algorithms
40(1)
3.11 Model: Errors in Algorithms
41(1)
3.11.1 Total Error
41(1)
3.12 Method: Optimizing with Known Error Behavior
42(1)
3.13 Method: Empirical Error Analysis
43(1)
3.14 Assessment: Experiment
44(3)
4 Integration
47(16)
4.1 Problem: Integrating a Spectrum
47(1)
4.2 Model: Quadrature, Summing Boxes
47(3)
4.3 Method: Trapezoid Rule
50(1)
4.4 Method: Simpson's Rule
51(1)
4.5 Assessment: Integration Error, Analytic
52(3)
4.6 Method: Gaussian Quadrature
55(3)
4.6.1 Scaling Integration Points
56(2)
4.7 Implementation: integ.f (.c)
58(1)
4.8 Assessment: Empirical Error Estimate
58(1)
4.9 Assessment: Experimentation
59(1)
4.10 Method: Romberg Extrapolation
59(4)
4.10.1 Other Closed Newton-Cotes Formulas
60(3)
Part II APPLICATIONS 63(280)
5 Data Fitting
63(20)
5.1 Problem: Fitting an Experimental Spectrum
63(1)
5.2 Theory: Curve Fitting
64(1)
5.3 Method: Lagrange Interpolation
65(2)
5.3.1 Example
66(1)
5.4 Implementation: lagrange.f (.c)
67(1)
5.5 Assessment: Interpolating a Resonant Spectrum
67(1)
5.6 Assessment: Exploration
68(1)
5.7 Method: Cubic Splines
69(2)
5.7.1 Cubic Spline Boundary Conditions
70(1)
5.7.2 Exploration: Cubic Spline Quadrature
71(1)
5.8 Implementation: Spline.f
71(1)
5.9 Assessment: Spline Fit of Cross Section
71(1)
5.10 Problem: Fitting Exponential Decay
72(1)
5.11 Model: Exponential Decay
72(1)
5.12 Theory: Probability Theory
73(2)
5.13 Method: Least-Squares Fitting
75(2)
5.14 Theory: Goodness of Fit
77(1)
5.15 Implementation: Least-Squares Fits, fit.f (.c)
78(1)
5.16 Assessment: Fitting Exponential Decay
79(1)
5.17 Assessment: Fitting Heat Flow
80(1)
5.18 Implementation: Linear Quadratic Fits
81(1)
5.19 Assessment: Quadratic Fit
82(1)
5.20 Method: Nonlinear Least-Squares Fitting
82(1)
5.21 Assessment: Nonlinear Fitting
82(1)
6 Deterministic Randomness
83(10)
6.1 Problem: Deterministic Randomness
83(1)
6.2 Theory: Random Sequences
83(1)
6.3 Method: Pseudo-Random-Number Generators
84(2)
6.4 Assessment: Random Sequences
86(1)
6.5 Implementation: Simple and Not random.f (.c); call.f (.c)
87(1)
6.6 Assessment: Randomness and Uniformity
87(1)
6.7 Assessment: Tests of Randomness, Uniformity
88(1)
6.8 Problem: A Random Walk
89(1)
6.9 Model: Random Walk Simulation
89(1)
6.10 Method: Numerical Random Walk
90(1)
6.11 Implementation: walk.f (.c)
91(1)
6.12 Assessment: Different Random Walkers
91(2)
7 Monte Carlo Applications
93(16)
7.1 Problem: Radioactive Decay
93(1)
7.2 Theory: Spontaneous Decay
93(1)
7.3 Model: Discrete Decay
94(1)
7.4 Model: Continuous Decay
95(1)
7.5 Method: Decay Simulation
95(2)
7.6 Implementation: decay.f (.c)
97(1)
7.7 Assessment: Decay Visualization
97(1)
7.8 Problem: Measuring by Stone Throwing
97(1)
7.9 Theory: Integration by Rejection
97(2)
7.10 Implementation: Stone Throwing, pond.f (.c)
99(1)
7.11 Problem: High-Dimensional Integration
99(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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