Computational Physics I

Monte Carlo, Schrodinger Equation, Cellular Automaton, vibrating string

Contains 5 types of Computational Physics applications with a brief theory

that explains the fundamentals for each case.

First: Fractals: the equations to obtain the tree and fern fractals is given and show their formation; the method to obtain Sierpinski gasket is explained and generated.

Second: vonNeuman rejection method for Monte Carlo integration of a given function, random points are generated, some lie inside the function others outside. If the device is rotated a new result is given.

Third: Cellular automaton: Wolfram cellular in which a new line of occupied cells depends on the previous line according to certain rules related to the occupancy of the tree previous cells above a new cell. Conway's Game of Life is programmed for two possibilities: random occupied cells are generated and see the evolution or select by hand the occupied cells and see the evolution according to the rules for survival, revival or death of the cells depending of the number of its neighboring occupied cells. packets for two cases: in one you select a potential which can be a rectangular barrier or a well and see the reflection and transmission of the packet. The other case is the motion a Gaussian wave packet in the harmonic oscillator potential.

Fifth: solution of the wave equation for a vibrating string with fixed ends and you can select the initial position of the string and see its motion.