Computational Physics
PHYS 410
Course Overview
This course provides a survey of techniques from numerical analysis and computational science applied to complex problems in physics. Through the use of MATLAB, I implemented various algorithms to simulate systems where analytical solutions are unavailable.
The curriculum covered floating-point arithmetic and error analysis, polynomial interpolation, root-finding for nonlinear equations, and finite difference approximations. A major focus was placed on:
- Differential Equations: Solving both ODEs and PDEs (Initial Value and Boundary Value problems).
- Advanced Methods: Implementing Monte Carlo methods and Fast Fourier Transforms (FFT).
- Physics Applications: Modeling systems in classical dynamics, quantum mechanics, and statistical mechanics.
Projects
Project 1: Galactic Collisions (The Toomre Model)
In this project, I implemented the Toomre Model to simulate the tidal interactions and dynamical evolution of colliding galaxies. By treating galaxies as central potentials surrounded by “test-particle” disks, I visualized the formation of tidal tails and bridge structures resulting from gravitational encounters.
Project 2: Numerical Solutions to the TDSE
I developed a solver for the Time-Dependent Schrödinger Equation (TDSE) in both 1D and 2D. To ensure numerical stability and unitarity, I utilized the Crank-Nicolson scheme. For the 2D case, I implemented the Alternating Direction Implicit (ADI) method to efficiently handle the dimensionality, allowing for the observation of wave packet scattering and tunneling.
Selected Coursework
While the projects were the highlight, these assignments focused on the rigorous implementation of fundamental algorithms.