Computational Physics

Aim

After completing the course, the student should be able to:

• explain basic concepts and theories in computational physics based on both classical and quantum mechanical methods
• explain the main components of the computational programs used to simulate materials and to find numerical solutions to many-particle problems in quantum mechanics
• use computer calculations and simulations to predict properties of materials and molecular systems.

Content

The course is about the theory and application of computer simulation of both classical and quantum mechanical many-body systems. Following a review of the principles of statistical mechanics underlying computer simulations, the Monte Carlo (MC) and Molecular Dynamics (MD) techniques are introduced. Topics discussed include MC integration, importance sampling, the Metropolis method, integration of equations of motion for many-body systems in MD, the Verlet algorithm, and MC and MD in various statistical ensembles. An introduction to calculus of variations and many-particle quantum mechanics is given, and then Hartree, Hartree-Fock, and Density Functional Theory methods are derived and discussed, as well as, ab-intio Molecular Dynamics. The course covers the underlying theoretical concepts of these topics, an overview of how they are implemented in computational software, and some examples of how the methods are used. The course has computer laborations with hands-on exercises for working with this type of computational software; generating data, analyzing, and visualizing the results.