COURSE GOALS: The principal objectives of the course Quantum physics of finite systems are the introduction of basic concepts and methods of quantum physics applied to microscopic finite systems, further development of acquired mathematical skills and their applications to selected physical problems, and the preparation of students for reasearch career in theoretical physics.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.2 demonstrate a thorough knowledge of advanced methods of theoretical physics including classical mechanics, classical electrodynamics, statistical physics and quantum physics
1.3 demonstrate a thorough knowledge of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena)
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1 identify the essentials of a process/situation and set up a working model of the same or recognize and use the existing models
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
2.5 perform numerical calculation independently, even when a small personal computer or a large computer is needed, including the development of simple software programs
4. COMMUNICATION SKILLS
4.3 develop the written and oral English language communication skills that are essential for pursuing a career in physics
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon completing the course Quantum physics of finite systems, students will be able to:
- apply the second quantization formalism when describing many-body systems;
- solve Schrödinger equation in the harmonic oscillator basis and calculate the necessary matrix elements by using the Moshinsky transformation;
- formulate the Hartree-Fock approximation and apply it when describing identical interacting fermions trapped in an external potential;
- formulate the Hartree-Fock-Bogoliubov approximation and apply it when describing identical interacting fermions trapped in an external potential;
- formulate the random phase approximation and apply it when describing identical interacting fermions trapped in an external potential;
- explain the mechanism of restoring symmetries that are broken on the mean-field level (e.g. translational symmetry);
- Second quantization formalism.
- Harmonic oscillator in quantum mechanics.
- Hartree-Fock approximation.
- Hartree-Fock-Bogoliubov approximation.
- Random phase approximation.
- Ground state correlations and restoration of broken symmetries.
REQUIREMENTS FOR STUDENTS:
Students are required to regularly attend classes, participate actively in solving problems and write a seminar paper.
GRADING AND ASSESSING THE WORK OF STUDENTS:
At the end of the course an oral exam is held for students who have successfully completed the requirements of the course.