Quantum Mechanics is often called the most successful theory in the
history of physics. However, only a few problems can be solved analytically.
This course will introduce numerical methods and computational
algorithms to study quantum mechanical systems, with examples taken from
different areas of physics. Numerical methods will include solution of ordinary and partial differential
equations, eigenvalue problems, matrix operations, solution of non-linear
functional equations, iterative methods, and Monte Carlo sampling. Quantum
mechanics issues addressed include solutions of semiclassical approximations, Hartree-Fock
and density functional equations for atoms and periodic crystals, introduction
to packages such as Gaussian for complex molecules, solutions of the time-dependent
Schrodinger equation, 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 selected topics,
including Bose-Einstein condensation, simulations in lattice gauge theories
and "Car-Parrinello" simulations of quantum systems using classical molecular 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 with a term paper and a presentation to the class.
Topics may range from more advanced computational
research projects to development of software for teaching quantum mechanics.
Recommended Textbook: "Computational Physics" by J. M. Thijssen,
Cambridge Press, 1999. Available in paperback.
Prerequisites: Quantum Mechanics at an advanced undergraduate level.
Elementary programming skills: students can program in
any language; programs provided in the course will be in Fortran 90 and C++.
Web Site: http://www.physics.uiuc.edu/research/ElectronicStructure/498CQM/
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Last Modified Jan. 4
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rmartin@uiuc.edu