Lecturer:
Associate professor John Ove Fjærestad (office: E5-126, email: john.fjaerestad@ntnu.no, phone: 93448)
Contents:
Occupation number representation for nonrelativistic fermionic and bosonic many-particle systems. Interacting electron gas. Lattice models for fermions and spins. Spin-wave theory of ferro- and antiferromagnets. Symmetries and conserved quantities. Broken symmetries, Goldstone modes. Green functions. Matsubara formalism. Many-particle perturbation theory and Feynman diagrams. Various applications. Relativistic quantum mechanics: The Klein-Gordon and Dirac equations.
Lectures:
Monday 10:15-12:00 and Friday 8:15-9:00 in E5-103.
Tutorials:
Friday 9:15-10:00 in E5-103 (starting in week 3).
As a pre-exam requirement, each student will present solutions to one or more tutorial problems
at at least one tutorial (more details will be provided later).
Quality assurance:
Information about the education quality assurance system
Exam:
Wednesday 21 May, 9:00-13:00.
You may bring:
- an approved calculator
- Rottmann: Matematisk formelsamling/Mathematische Formelsammlung
- Barnett and Cronin: Mathematical Formulae for Engineering and Science Students
Pre-exam Q&A session:
Friday 16 May at 10:15 in E5-103.
Curriculum:
The curriculum ("pensum") for the exam is based on the material that has been covered in lectures, plus the written solutions to the tutorial problems. For the lecture material one may alternatively use the following notes/sources:
- Second quantization
- Second quantization representation for the Hamiltonian of an interacting electron gas
- Noninteracting electrons. The free electron gas
- Tight-binding model for electrons in a crystal
- The Hubbard and Heisenberg models, spin-wave theory of ferro- and antiferromagnets, broken symmetry and Goldstone modes
- Transformations and symmetries in quantum mechanics
- Introduction to Green functions and many-body perturbation theory (except Secs. 4.9 and 4.10)
- The Klein-Gordon equation: Sec. 17.1.1 in Hemmer's "Kvantemekanikk".
- The Dirac equation: Sec. 17.2 in Hemmer, except Sec. 17.2.4.c about helicity.
Note that the following topics which were discussed in lectures (some of them only briefly) are not examinable:
- the material on Bloch and Wannier states discussed before the tight-binding model
(but note that the material on the tight-binding model is examinable, cf. notes above)
- the detailed derivation (using projection operators) of the S=1/2 Heisenberg antiferromagnetic model from the
half-filled Hubbard model in the strong-interaction limit
- the Mermin-Wagner theorem
- aspects of broken symmetry that are not covered in Sec. 6 of the magnetism notes (but, to be clear, the material in that section is examinable)
- the Kubo formula for the conductivity (Secs. 4.9 and 4.10 in the
Green function notes)
In the tutorials, the following topics are not exam relevant:
- Problem 1 in Tutorial 4
- Issues related to the projection operators P in problem (e) in
Tutorial 5.
The curriculum this year is very similar to that for the
2013 version of the course. A brief summary
of the minor differences between the notes above and last year's
versions can be found here.
Resources:
Main resources:
- Notes by the lecturer. Notes for the various
sections will be identical or similar to those used in the 2013 version of the course.
- Ch. 17 on relativistic wave equations in "Kvantemekanikk" by P. C. Hemmer (Tapir, 2005).
Supporting resources:
There is no single textbook that covers all the material that will be discussed in the course. Much of the material on non-relativistic quantum many-particle systems is covered in "Many-body quantum theory in condensed matter physics" by Bruus and Flensberg (Oxford, 2004), which is the main recommended textbook for this part of the course. Another recent textbook in the same area that may be useful is "Condensed matter field theory" by Altland and Simons (2nd ed., Cambridge, 2010). An old classic is "Quantum theory of many-particle systems" by Fetter and Walecka from 1971 which is available in a non-expensive paperback version (Dover, 2003). The main reference on the quantum magnetism material is "Interacting electrons and quantum magnetism" by Auerbach (Springer, 1994). Other references may be provided later.
Tutorial sets:
| Tutorial | Date | Presenter | Problems | Solution |
|---|---|---|---|---|
| 1 | 17 Jan | Toni Müller | |
|
| 2 | 24 Jan | Vigdis Toresen | |
|
| 3 | 31 Jan | Jonas Kjellstadli | |
|
| 4 | 7 Feb | Kilian Mitterweger | |
|
| 5 | 14 Feb | Noemie Jourdain | |
|
| 6 | 21 Feb | Tristan Müller | |
|
| 7 | 28 Feb | Sverre Gulbrandsen | |
|
| 8 | 7 Mar | Camilla Espedal | |
|
| 9 | 14 Mar | Ane Nordlie Johansen | |
|
| 10 | 21 Mar | --- | |
|
| 11 | 28 Mar | Laura Friedeheim Daniel Wennberg |
|
|
| 12 | 4 Apr | --- | |
|
| 13 | 11 Apr | Lynn Vera Meissner | |
|
Other:
Past exams
2013 course website