Computational Physics using MATLAB.pdf

【核心代码】

Table of Contents
Preface........................................................................................................................................6
1. Uranium Decay.......................................................................................................................7
3. The Pendulum........................................................................................................................9
3.1 Solution using the Euler method......................................................................................9
3.1.1 Solution using the Euler-Cromer method.................................................................... 10
3.1.2 Simple Harmonic motion example using a variety of numerical approaches.............11
3.2 Solution for a damped pendulum using the Euler-Cromer method............................. 16
3.3 Solution for a non-linear, damped, driven pendulum :- the Physical pendulum, using
the Euler-Cromer method.................................................................................................... 18
3.4 Bifurcation diagram for the pendulum .........................................................................24
3.6 The Lorenz Model ..........................................................................................................26
4. The Solar System .................................................................................................................28
4.1 Kepler’s Laws..................................................................................................................28
4.1.1 Ex 4.1 Planetary motion results using different time steps .........................................30
4.2 Orbits using different force laws ....................................................................................35
4.3 Precession of the perihelion of Mercury. .................................................................... 40
4.4 The three body problem and the effect of Jupiter on Earth ..........................................48
4.6 Chaotic tumbling of Hyperion.......................................................................................53
5. Potentials and Fields........................................................................................................... 60
5.1 Solution of Laplace’s equation using the Jacobi relaxation method. ........................... 60
5.1.1 Solution of Laplace’s equation for a hollow metallic prism with a solid, metallic inner
conductor. ............................................................................................................................63
5.1.2 Solution of Laplace’s equation for a finite sized capacitor ........................................66
5.1.3 Exercise 5.7 and the Successive Over Relaxation Algorithm.......................................70
5.2 Potentials and fields near Electric charges, Poisson’s Equation.................................... 75
6. Waves ...................................................................................................................................78
6.1 Waves on a string...........................................................................................................78
6.1.1 Waves on a string with free ends .................................................................................81
6.2 Frequency spectrum of waves on a string .....................................................................83
7. Random Systems..................................................................................................................87
7.1 Random walk simulation................................................................................................87
7.1.1 Random walk simulation with random path lengths...................................................89
10. Quantum Mechanics .......................................................................................................... 91
10.2 Time independent Schrodinger equation. Shooting method....................................... 91
Kevin Berwick Page 3
10.5 Wavepacket construction .............................................................................................93
10.3 Time Dependent Schrodinger equation in One dimension. Leapfrog method............95
10.4 Time Dependent Schrodinger equation in two dimensions. Leapfrog method...........99