Concepts in Solid State Theory (FSI-9TPL)

Academic year 2022/2023
Supervisor: prof. RNDr. Petr Dub, CSc.  
Supervising institute: ÚFI all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The aim of the course is to extend, supplement or deepen the knowledge of PhD students in the physics of solids in areas related to the topic of his / her dissertation.
Learning outcomes and competences:
PhD student gains insight into concepts of the theory of solids, such as the application of group theory, quasiparticle concept or application of Green functions.
Prerequisites:
Solid state physics course
Course contents:
Group-theoretical methods in solid state physics. Collective excitations in solids. Green’s functions for solid state physics. Depending on the doctoral thesis, the topics may be modified.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline, or through individual discussions with students.
Assesment methods and criteria linked to learning outcomes:
The doctoral student prepares an essay on the topic related to the dissertation and then a debate is held to demonstrate the doctoral student's orientation in the concepts of condesed matter physics.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture PhD student, who has completed inroductory solid state physics course, gains insight into concepts of the theory of solids, such as the application of group theory, quasiparticle concept or application of Green functions. Depending on the doctoral thesis, the topics may be modified.

Group-theoretical methods in solid state physics. Collective excitations in solids. Green’s functions for solid state physics. Depending on the doctoral thesis, the topics may be modified.
Group-theoretical methods in solid state physics.
Symmetry in physics. Group representations. Groups and quantum mechanics: Hamiltonian symmetry and classification of the energy levels, perturbation theory – splitting of energy levels, selection rules. Symmetry of crystals, spatial groups and their representations. Group theory and electronic structure of solids. Group theory and crystal lattice vibrations.

Green’s functions for solid state physics.
Green’s functions in the theory of differential equations. Oneparticle Green’s functions. Green's function and the density of states. Application of Green’s functions: scattering theory, crystals with point defects.
Literature - fundamental:
1. J. Celý, Kvazičástice v pevných látkách. VUTIUM, Brno 2004.
2. O. Litzman, I. Sekanina, Užití grup ve fyzice. Academia, Praha 1982.
3. J. M. Ziman, Principles of the Theory of Solids. CUP 1972.
4. S. C. Altman, Band theory of Solids. An introduction from the point of view of symmetry. Clarendom Press. Oxford 1991.
5. M. S. Dresselhaus, G. Dresselhaus, Ado Jorio, Group Theory: Application to the Physics of Condensed Matter. Springer 2008.
6. E. N. Economu, Green’s functions in quantum mechanics. Springer 1979.
7. L. Bányai, A compendium of Solid state theory, Springer, 2018
8. M. L. Cohen, S. G. Louie, Fundamentals of Condesed matter physics. CUP, 2016
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D-FIN-K combined study --- -- DrEx 0 Recommended course 3 1 W
D-FIN-P full-time study --- -- DrEx 0 Recommended course 3 1 W