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763312A Quantum mechanics I, 10 ECTS cr 
Code 763312A  Validity 01.01.1950 -
Name Quantum mechanics I  Abbreviation Quantum mechani 
Scope10 ECTS cr   
Type Intermediate Studies Discipline3253 Theoretical Physics 
  Grading1 - 5, pass, fail 
Unit Field of Physics 

ECTS Credits 

10 ECTS credits

Language of instruction 

Finnish / English depending on the audience


3rd autumn

Learning outcomes 

The most important goal of the course is the development of a quantum mechanical frame-of-mind. After the course, the student knows the postulates of quantum mechanics and can solve the Schrödinger equation in such one- and three-dimensional problems that have important applications in condensed matter physics and in atomic, nuclear and molecular physics. The student will also learn to derive the uncertainty principle and use it to interpret what happens in a quantum mechanical measurement.


Quantum mechanics, together with the general theory of relativity, lays the foundation for the modern scientific understanding of the nature. Recent developments in nanotechnology has also brought quantum-based applications into our everyday lives. However, the greatest influence quantum mechanics brings is on how we understand and interpret the behavior of the basic building blocks of nature. One of the interesting results of quantum mechanics is the uncertainty principle which means, for example, that a particle does not possess well defined position and velocity at a given time. This has far-reaching consequences in our understanding of the structure of matter, and even of the present amount and distribution of galaxies in the known universe. The inherent indeterminacy in the classical state of the particles implies that the microscopic particles have to be described with the so-called wave function, which determines the probability density of finding the particle at an arbitrary location. The course begins with the introduction of the basic principles and postulates of quantum mechanics. As an example, several one-dimensional problems for the time-evolution of the wave function are solved. The uncertainty principle is derived in its general form, and applied to the simultaneous measurement of position and velocity. In three-dimensional problems, spherical symmetry is connected with the angular momentum. The corresponding operators and quantum numbers are derived. As an example, the quantized energy states of hydrogen atom are solved. The general formulation of quantum mechanics in terms of abstract Hilbert space and its linear transformations is presented, and shown to be equivalent with the wave function formalism. The properties of the general theory are illustrated in terms of the two quantum paradigms: the two-level system and the
harmonic oscillator.

Mode of delivery 

Face-to-face teaching

Learning activities and teaching methods 

Lectures 50 h, 12 exercises (á 3 h), self-study and examination 184 h

Target group 

Compulsory for theoretical physicists and physicists. Also for the other students of the University of Oulu.

Prerequisites and co-requisites 

Atomic physics (766326A) and knowledge of linear algebra and differential equations.

Recommended optional programme components 

No alternative course units or course units that should be completed simultaneously.

Recommended or required reading 

J. Tuorila: Kvanttimekaniikka I (2013, in Finnish). D. Griffiths: Introduction to Quantum Mechanics (2005).

Assessment methods and criteria 

Two written intermediate examinations or one final examination.

Read more about assessment criteria at the University of Oulu webpage.


Numerical grading scale 0 – 5, where 0 = fail

Person responsible 

Matti Alatalo

Working life cooperation 

No work placement period


Current and future instruction
Functions Name Type ECTS cr Teacher Schedule
registration period has not begun Quantum mechanics I  Course  10  Matti Alatalo  02.09.20 -07.12.20

Future examinations
No examinations in WebOodi