Hohenberg-Kohn theorem
Hellmann-Feynman theorem
Local-density approximation
The general variational principle
The Hartree-Fock method
Pairing correlation and the BCS model
Nuclear interaction and nuclear superfluidity
The Hartree-Fock-Bogoliubov theory
Richardson model
Tamm-Dancoff and Random-Phase approximations
Nuclear collective motion
The main aim of the course is to understand the basic concepts in many-body physics and energy density functional theory. When completing the course, the students should be able to use the second quantization, solve the Hatree-Fock equations and the BCS equation for superconductivity. They should also be able to describe advanced approaches to treat the pairing problem including generalized seniority model, the Richardson model as well as the Hartree-Fock-Bogoliubov approach. They will be able to apply the pairing models to analze the properties of complex quantum systems including atomic nuclei. The course aims also at understanding and implementing numerical methods. To achieve this the students will be provided with both basic and advanced numerical tools for solving complicated many-body problems. They should be able to implement one or several of those tools and understand the results. The students are also expected to write their own codes for solving complex systems in a simple way and write the scientific report in a standard manner.
Admitted to PhD studies in Physics, Biological Physics, or related fields of study.
P. Ring and P. Schuck, Nuclear Many body problem, (Springer, Berlin) 1980 (Chap. 5-8).
D. Rowe and JL Wood, Fundamentals of Nuclear Models: Foundational Model and own material.
If the course is discontinued, students may request to be examined during the following two academic years.
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
To pass the course the students should give 1-2 open seminars on the subject and hand in a study report. In both cases the students should demonstrate that they have obtained good understanding of the subject and be able to apply their knowledge to practial problems and answer the questions and comments raised by the teacher and other students in a proper way.
