Parallel Computational Approaches for Solvng Schroedinger's Equation
The goal for our project this year is to find the most efficient way of solving Schroedinger's equation. We will compare the finite difference and Monte Carlo techniques on a multi-processor machine. Schroedinger's equation is a second order differential equation that determines a particle's energy. It is used for describing all quantum-mechanical problems. The finite difference method is a structured computational technique that converts mathematical derivatives into difference equations on a grid. Monte Carlo approaches rely on a random generation of function values as a means by which to solve the problem. We will test each method with a single processor and with a parallel processor system on an IBM SP-2. We will determine efficiency by comparing the computational time and accuracy of the solution. To test our software we will solve the "particle in a box" problem in which a particle is confined to movement inside a two or three dimensional box. Once we determine the more efficient computational approach for solving Schroedinger's equation, we will apply that technique to more complex problems.