计算物理

preface

about the authors

1 a first numerical problem

1.1 radioactive decay

1.2 a numerical approach

1.3 design and construction of a working program:codes and pse docodes

1.4 testing your program

1.5 numerical considerations

1.6 programming guidelines and philosophy

2　realistic projectile motion

2.1 bicycle racing:the effect of air resistance

2.2 projectile motion:the trajectory of a cannon shell

2.3 baseball:motion of a batted ball

2.4 throwing a baseball:the effects of spin

2.5 golf

3 oscillatory motion and chaos

3.1 simple harmonic motion

3.2 making the pendulum more interesting:adding dissipation, nonlinearity, and a driving force

3.3 chaos in the driven nonlinear pendulum

3.4 routes to chaos:period doubling

.　3.5 the logistic map:why the period doubles

3.6 the lorenz model

3.7 the billiard problem

3.8 behavior in the frequency domain:chaos and noise

4　the solar system

4.1 kepler's laws

4.2 the inverse-square law and the stability of planetary orbits

4.3 precession of the perihelion of mercury

4.4 the three-body problem and the effect of jupiter on earth

4.5 resonances in the solar system:kirkwood gaps and planetary rings

4.6 chaotic tumbling of hyperion

5 potentials and fields

5.1 electric potentials and fields:laplace's equation

5.2 potentials and fields near electric charges

5.3 magnetic field produced by a current

5.4 magnetic field of a solenoid:inside and out

6 waves

6.1 waves:the ideal case

6.2 frequency spectrum of waves on a string

6.3 motion of a(somewhat)realistic string

6.4 waves on a string(again):spectral methods

7 random systems

7.1 why perform simulations of random processes?

7.2 random walks

7.3 self-avoiding walks

7.4 random walks and diffusion

7.5 diffusion, entropy, and the arrow of time

7.6 cluster growth models

7.7 fractal dimensionalities of curves

7.8 percolation

7.9 diffusion on fractals

8 statistical mechanics, phase transitions, and the ising model

8.1 the ising model and statistical mechanics

8.2 mean field theory

8.3 the monte carlo method

8.4 the ising model and second-order phase transitions

8.5 first-order phase transitions

8.6 scaling

9 molecular dynamics

9.1 introduction to the method:properties of a dilute gas

9.2 the melting transition

9.3 equipartition and the fermi-pasta-ulam problem

10 quantum mechanics

10.1 time-independent schrsdinger equation:some preliminaries

10.2 one dimension:shooting and matching methods

10.3 a matrix approach

10.4 a variational approach

10.5 time-dependent schr6dinger equation:direct solutions

10.6 time-dependent schr6dinger equation in two dimensions

10.7 spectral methods

11 vibrations,waves,and the physics of musical instruments

12 interdisciplinary topics

appendices

a ordinary differential equations with initial values

b root finding and optimization

c the fourier transform

d fitting data to a function

e numerical integration

f generation of random numbers

g statistical tests of hypotheses

h solving linear systems

index

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