qtiptip/fys3150

FYS3150 - Computational Physics

Introduction

This repository is ment to contain various files related to the course Computational Physics (FYS3150) held at the University of Oslo, fall 2015.

I will hopefully spend some time updating this readme as more work is done in the course, and hopefully all code present in the repository should have clear instructions on how to be ran.

Course outline

The course has five mandatory projects where it is required to upload the associated report as well as source code.

List of Projects

Project 1

We solve the Poisson equation in its one-dimensional form for a spherically symmetric system. The problem reduces to that of a tridiagonal matrix problem and we implement the tridiagonal matrix algorithm in order to solve this. We also discuss nuances of the numerical approximation used in order to discretize our problem.

Project 2

We examine the Schrödinger equation for two electrons in a harmonic oscillator well. It can be shown that this can be formulated as an eigenvalue problem, and we solve this problem using the Jacobi method. We consider the system for various choices of the different parameters and analyze under what conditions our results are reasonable. Bogus alert! Me not having taken physics, I'm probably way off on some of my points.

Project 3

We consider three numerical integration methods for computing the ground state correlation energy between two electrons in a hydrogen atom. Among the methods considered are Guassian-Legendre quadrature, Gaussian-Laguerre quadrature and Monte Carlo-integration.

Project 4

We look at the Ising model for magnetic systems with no external magnetic field. The metropolis algorithm is well suited for this kind of statistical analysis, and will be used in this project. We first derive some analytical results specific to the 2x2-case and compare these to our numerical computations. The code is parallellized using OpenMPI which lets you run the code on several clusters.

Project 5

We simulate argon using face centered cubic lattice, the Lennard-Jones potential and the Velocity Verlet time integrator. The melting temperature of argon is measured to be somewhere around 300K. We also look at the energy conservation of Velocity Verlet and how it compares to the Euler-Cromer algorithm.