compphys

Several exercise simulations for a computational physics course.

Exercise 1

A few simple warmup problems to get everybody up to speed.

1. Simple matrix operations
2. Computing the Chebyshev polynomials using iteration.
3. Integer Overflow

Exercise 2

1. Random walks in one dimension
2. Event-based simulation of an EPRB experiment. Simulate quantum behaviour without solving the Schrödinger equation.

Exercise 3

Simulation of the Ising model of ferromagnetism for one and two dimensions using the Metropolis-Monte-Carlo algorithm. The two-dimensional Ising model shows phase transitions.

Exercise 4

Solving the Newtonian equations of motion using different algorithms such as

• Simple Euler
• Symplectic Euler
• Velocity Verlet

Exercise 5

Maxwell's laws of electromagnetism in one dimension using Yee's algorithm

Exercise 6

Solving the diffusion equation using a product formula approach and comparing it to random walks.

Exercise 7

Solver for the one-dimensional Schrödinger equation. Test case: Tunneling of a Gaussian wave packet through a tunnel barrier

Exercise 8

Solver for Bloch's equations for the behavior of ensembles of non-interacting spin-1/2 nuclei in a magnetic field used in NMR/MRI and quantum information