Introduction to mathematical physics, fall 2010
Spectral theory
Lecturer
Scope
10 cu.
Type
Advanced studies. Very suitable as a continuation of Introduction to functional analysis (Funktionaalianalyysin peruskurssi)
Description
The course focuses on derivation and applications of spectral theory of operators on a Hilbert space. The mathematical topics will include Banach algebras and spectral measures of unbounded operators, and applications will be mainly chosen from physics, in particular, from quantum mechanics
Prerequisites
Basic measure theory and functional analysis
Course announcements
- The course and the grading are now finished. The marked exams can be collected from the lecturer.
- Problem sheets and lecture notes can be downloaded from below. For solutions to the problems, please send e-mail to the instructor.
Lectures
Tue 14-16 and Thu 14-16, Exactum room C123. On weeks 36-41, 44, and 46-50
Bibliography
- Course lecture notes
- W. Rudin, Functional Analysis, McGraw-Hill, 2nd edition, 1991
- M. Reed, B. Simon, Methods of Modern Mathematical Physics I: Functional Analysis & II: Fourier Analysis, Self-Adjointness, Academic Press, 1980 & 1975
- G. Teschl, Mathematical Methods in Quantum Mechanics; With Applications to Schrödinger Operators, Graduate Studies in Mathematics 99, Amer. Math. Soc., 2009
- T. Kato, Perturbation Theory for Linear Operators (Classics in Mathematics), Springer, 2008
- O. Bratteli, D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 1 & 2, Springer, 2002 & 2002
Registration
Did you forget to register? What to do.
Exercise groups
| Group | Day | Time | Place | Instructor |
|---|---|---|---|---|
| 1. | Fri | 10-12 | C122 | Peng Mei |
Problem sheets
Lecture notes
| Held on | Download | |
|---|---|---|
| 13. | 2.11. | Lect13.pdf |
| 14. | 4.11. | Lect14.pdf |
| 15. | 16.11. | Lect15.pdf |
| 16. | 18.11. | Lect16.pdf |
| 17. | 23.11. | Lect17.pdf |
| 18. | 25.11. | Lect18.pdf |
| 19. | 30.11. | Lect19.pdf |
| 20. | 2.12. | Lect20.pdf |
| 21. | 7.12. | Lect21.pdf |
| 22. | 9.12. | Lect22b.pdf |
| 23.* | (14.12.) | Lect23.pdf |
| Held on | Download | |
|---|---|---|
| 1. & 2. | 7. & 9.9. | Lect1-2.pdf |
| 3. | 14.9. | Lect3.pdf |
| 4. | 16.9. | Lect4b.pdf |
| 5. | 21.9. | Lect5.pdf |
| 6. | 23.9. | Lect6.pdf |
| 7. | 28.9. | Lect7.pdf |
| 8. | 30.9. | Lect8.pdf |
| 9. | 5.10. | Lect9.pdf |
| 10. | 7.10. | Lect10.pdf |
| 11. | 12.10. | Lect11.pdf |
| 12. | 14.10. | Lect12b.pdf |