Uusi opinto-opas (sisältäen myös opetusohjelmat) lukuvuodelle 2018-2019 sijaitsee osoitteessa https://opas.peppi.utu.fi . Tältä sivustolta löytyvät enää vanhat opinto-oppaat ja opetusohjelmat.

The new study guide (incl. teaching schedules) for academic year 2018-2019 can be found at https://studyguide.utu.fi. This site contains only previous years' guides.

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Arkistoitu opetussuunnitelma 2016–2018
Selaamasi opetussuunnitelma ei ole enää voimassa. Tarkista tiedot voimassa olevasta opetussuunnitelmasta.
KEMI6505 Quantum mechanics and molecular symmetry 5 op
Organised by
Person in charge
Jukka Lukkari
Preceding studies
Intermediate physical chemistry I and II (Fysikaalinen kemia I ja II), recommended Mathematics and Physics for chemists, recommended

Learning outcomes

This course is intended as an introduction to more advanced topics to chemistry students with no other background in quantum mechanics except the intermediate chemistry courses. It introduces students to the theoretical structure of quantum mechanics and to the role of molecular symmetry and its description using group theory. After the course, the student understands the basic mathematical structure of quantum mechanics, its fundamental results in connection with chemistry, and can apply the knowledge to simple chemically relevant problems. The student also understands the principle of molecular symmetry and can apply it to simple chemical problems involving quantum mechanics and vibrational spectroscopy. The course gives background knowledge needed in more advanced courses on quantum chemistry.


The mathematical foundations of quantum mechanics (axioms, state vectors and vector spaces, Dirac formalism, operators, matrices), time evolution of systems, expectation values, uncertainty relations, quantum mechanical angular momentum (general theory, orbital angular momentum, spin), techniques of approximation (perturbation, variation principle), molecular symmetry and group theory, applications of group theory in chemistry (vanishing integrals, orbital symmetry, vibrational spectroscopy).

Teaching methods

Teaching method Contact Online
Lectures 40 h 0 h

Lectures, homework problems

Teaching language


Modes of study

Option 1
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
Written exam
  • In English


Numeric 0-5.

Recommended year of study

4. year autumn
5. year autumn

Autumn 2016

Study materials

Lecture notes and corresponding chapters in the textbook Peter Atkins. Julio de Paula, Atkins’ Physical Chemistry, 10thed., OUP, Oxford, GB, 2014.

Belongs to following study modules

Kemian laitos
Kemian laitos
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Implementation details are unavailable.
Kemian laitos
MDP in Materials Science