This course will introduce numerical
methods and computational algorithms to study one-particle and many-particle
quantum mechanical systems. Emphasis will be on atomic, molecular and solid
state systems, but examples will also be taken from other areas of physics.
Numerical methods will include solution of ordinary and partial differential
equations, eigenvalues problems, matrix operations, solution of non-linear
functional equations, iterative methods, and Monte Carlo sampling. Quantum
mechanics issues addressed include solutions of semiclassical approximations,
single particle time-independent Schrodinger equation, the Hartree-Fock
and density functional equations for atoms and periodic crystals, introduction
to packages such as Gaussian for complex molecules, solutions of time-dependent
Schrodinger equation in one space dimension, and finding the ground state
of the many-body Schrodinger equation by propagation in imaginary time
using Monte Carlo methods. We will also introduce selected current topics,
such as "Car-Parrinello" simulations of quantum systems using classical
Newtonian dynamics.
Homework will involve derivations of important steps in numerical
algorithms, understanding of ideas in quantum mechanics, writing computer
programs, and calculations with existing codes.
An integral part of the course will be for each student to carry
out a project and write a term paper that will be included in the collected
papers for the class. These may range from more advanced computational
research projects to development of software for teaching quantum mechanics.
Recommended Textbook: Koonin, S. E. & Meredith, D. C., "Computational
Physics - Fortran Version",Addison-Wesley, 1990. General Methods of computational
physics mainly oriented toward quantum mechanics. (Revised Fortran codes
related to ones described in the text will be used and developed during
the course. Students may write programs in C.)
Prerequisites: Elementary programming. Quantum Mechanics at an advanced
undergraduate level.
Web Site: http://www.physics.uiuc.edu/groups/rmweb/498/
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