Quantum Statistics, spring 2018

Quantum Statistics (537005, 5cr) 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 important topics covered during the course 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 bilingual: lectures are given in Finnish, but the homework problems are provided 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. It will be possible to take the final exam in either language.


Mondays and Tuesdays 12.15-14.00 in A315. The first lecture takes place on March 12.

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 D106. The first exercise session takes place on March 23.

Teaching Assistant: Pyry Wahlman, pyry.wahlman@helsinki.fi.

The home work problem sets are published on this page on Sundays: Problem sets 1, 2, 3, 4, 5, 6. Written solutions should be returned to the designated mail box of the course (to be found in the exercise room on the 2nd floor of Physicum) by the Monday of the following week. The solutions are graded, and they make up 1/4 of the final grade of the course.

Course results

The course results are now available here.

Timetable and lecture notes

The lectures will follow the rough timetable given below. Online lecture notes will be posted here prior to the lectures, so that the students will be able to familiarize themselves with the material beforehand.

Week 1 (12.-13.3.): Basics of quantum mechanics, Fock space, density operator, density of states
Week 2 (19-20.3.): Quantum mechanical ensemble theory
Week 3 (26.-27.3.): Connection to thermodynamics, free spin systems
Easter break for 29.3.-4.4.
Week 4 (9.-10.4.): Diatomic ideal gas, boson and fermion statistics
Week 5 (16.-17.4.): Boson systems: Bose-Einstein condensation, photon gas, black body radiation
Week 6 (23.-24.4.): Fermion systems: cold degenerate Fermi gas, Pauli's paramagnetism, relativistic systems
Week 7 (8.5.): 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