FYS-KJM9480 – Quantum mechanics for many-particle systems

Course content

This course gives an introduction to the quantum mechanics of many-body systems and the computational methods relevant for many-body problems in such diverse areas as atomic, molecular, solid-state and nuclear physics, chemistry and materials science. A theoretical understanding of the behavior of quantum-mechanical many-body systems - that is, systems containing many interacting particles - is a considerable challenge in that no exact solution can be found; instead, reliable methods are needed for approximate but accurate simulations of such systems on modern computers. Besides the intrinsic theoretical interest in such methods, they are of great pratical importance in modern research and industry, in fields such as semi-conductor physics, materials science and pharmaceutics.

The aim of this course is to present some of the most widely used many-body methods, starting with the underlying formalism of second quantization and with emphasis on non-relativistic theory. The topics covered are the Feynman diagram rules, microscopic mean-field theories (Hartree-Fock and Kohn-Sham theories), many-body perturbation theory, large-scale diagonalization methods, coupled-cluster theory, and Green's function approaches. Both fermionic and bosonic systems are discussed. Selected physical systems from various fields such as chemistry, solid-state physics and nuclear physics are studied, depending on the background and interests of the participants.

Learning outcome

The student should be able to apply these methods to selected physical systems as presented. He/she should have a clear understanding of central many-body methods.

Admission

PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Prerequisites

Recommended previous knowledge

A good background in mathematics is needed. Courses like FYS3110 – Quantum Mechanics or FYS-MENA3110 – Kvantenanofysikk (discontinued) are recommended.