ECTS Credits |
10 ECTS credits |

Language of instruction |
Finnish / English depending on the audience |

Timing |
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. |

Contents |
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. |

Grading |
Numerical grading scale 0 – 5, where 0 = fail |

Person responsible |
Matti Alatalo |

Working life cooperation |
No work placement period |