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.