Quantum Statistics, spring 2017

Quantum Statistics is a master level Theoretical Physics course at the University of Helsinki that concentrates on the quantum aspects of statistical physics and directly follows the BSc course Statistical Mechanics. The most central topics covered during the classes include quantum mechanical ensemble theory, boson and fermion statistics, and common examples of physical systems exhibiting these statistics.

Previous knowledge of classical statistical mechanics and the basics of quantum mechanics will be assumed in the lectures. In particular, the students are expected to have successfully passed Statistical Mechanics and Quantum Mechanics I, as well as all the prerequisite classes of these courses.

The course is lectured in English, and both the homework problems and final exam are given in English. The lecture notes and course book are in Finnish, but handwritten notes in English (from a previous year) as well as a list of international textbooks are provided below.


Mondays 14.15-16.00 and Tuesdays 12.15-14.00 in E205. The first lecture takes place on March 13. Note that due to the Easter break and May Day, there will be no lectures on 17.-18.4 and 1.5.

Lecturer: Aleksi Vuorinen, A322, aleksi.vuorinen@helsinki.fi.

The course book is Statistinen fysiikka (J. Arponen and J. Honkonen, Limes ry, 2000). Additional recommended reading includes:


Fridays 14.15-16.00 in E205. The first exercise session will be held on March 24. Note that due to the Easter break, no exercise session will take place on 14.4.

Teaching Assistant: Eemeli Annala, A313, eemeli.annala@helsinki.fi.

The home work problem sets are published on this page on Tuesdays: Problem sets 1, 2, 3, 4, 5, 6. Written solutions should be returned either directly to the lecturer or to his mailbox by the Tuesday of the following week. The solutions are graded, and they make up 1/4 of the final grade of the course.

Exam and results

The final exam will be held on Tuesday, May 9 at 13.00-17.00 in the lecture hall E207 of Physicum. The problems will be given both in Finnish and English, and it is ok to answer in either language.

The exam will cover all the material presented in the (Finnish) lecture notes as well as the chapters of the course book referred to in these notes. The lecture notes in English provided below cover almost all of this material, but the students are encouraged to check the Finnish lecture notes for individual items that might go beyond the English ones.

No "cheat sheets" are allowed in the exam, but a pocket calculator (not containing any stored material related to this class) is ok. All necessary lengthy formulas will be printed on the exam sheet.

The course results are now available here.

Timetable and lecture notes

The lectures follow the rough outline given below. Lecture notes will be linked here as the course progresses; a given week's notes are typically posted right after Tuesday's lecture.

Week 1 (13.-14.3.): Basics of quantum mechanics, Fock space, density operator, density of states
Week 2 (20-21.3.): Quantum mechanical ensemble theory
Week 3 (27.-28.3.): Review of Fock space and ensembles, connection to thermodynamics, free spin systems
Week 4 (3.-4.4.): Diatomic ideal gas, boson and fermion statistics
Week 5 (10.-11.4.): Boson systems: Bose-Einstein condensation, photon gas, black body radiation
Easter break for 17.-18.4.
Week 6 (24.-25.4.): Fermion systems: cold degenerate Fermi gas, Pauli's paramagnetism, relativistic systems
Week 7 (2.5.): Review of course material
Week 8 (9.5.): Final exam at 13.00-17.00 in E207

Lecture notes from 2015, covering ~90% of the course material and roughly following the above syllabus (in English):

Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7