Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


After completing the course the student

  1. Is familiar with the structure and postulates of quantum mechanics
  2. Can differentiate between the terms quantum-mechanical state and wavefunction
  3. Can solve the eigenstates and eigenvalues of the Schrödinger equation in simple situations and knows how to generalize the computation to situations where analytical solution is challenging. 
  4. Can integrate the quantum evolution and the expectation values of physical quantities for simple systems.
  5. Can apply creation and annihilation operators to analyze one-dimensional harmonic oscillator.
  6. Can solve the eigenstates of the one-dimensional harmonic oscillator. 
  7. Can predict measurent probabilities from a given quantum state.
  8. Can apply perturbation theory to compute eigensolutions in a situation where analytical solutions is challenging. 

Credits: 5

Schedule: 26.10.2020 - 08.12.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Tapio Ala-Nissilä, Mikko Möttönen

Teacher in charge (applies in this implementation): Tapio Ala-Nissilä, Mikko Möttönen

Contact information for the course (valid 06.10.2020-21.12.2112):

Aravind Babu (course assistant, whole course,, Mikko Möttönen (lecturing first 3 weeks), Tapio Ala-Nissilä (lecturing last 3 weeks)

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    Postulates of quantum mechanics. Operators, eigenvalues and eigenfunctions. Expectation values and variance. Schrödinger equation. Properties of Hermitian operators. Qubit (two-level system). The superposition principle. Heisenberg's uncertainty principle. Commutator relations. Conserved quantities. Dirac notation. Hilbert space. Free particle and continuum energy spectrum.  Particle in a potential well and discrete energy spectrum. Creation and annihilation operators and their relation to one-dimensional harmonic oscillator. The temporal evolution of quantum states and expectation values. Perturbation theory. Time development of expectation values (Ehrenfest's principle). The density matrix. Rotating frame. 

  • Applies in this implementation:

    We use heavily Dirac notation and tend to take a modern path on learning quantum mechanics. Thus we do not start from wavefunctions but show how they appear in certain cases from quantum states in the Hilbert space. We tend to put more emphasis here than in usual first courses in quantum mechanics to qubits which are important for quantum technology. 

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Teaching methods: lectures and exercises 

    Assessment methods: exercises and exam

  • Applies in this implementation:

    An exam will be organized at the end of the course with maximum of 30 points. Successfully completed exercises will add a maximum of 6 points bonus to the points obtained from the exam. 

  • Valid 01.08.2020-31.07.2022:

    Lectures: 24 h, exercises: 12 h, exam: 3 h + independent work


Study Material
  • Valid 01.08.2020-31.07.2022:

    Several options for recommened reading (R. L. Liboff: Introductory Quantum Mechanics, Ballentine: Quantum Mechanics - A Modern Development, Griffiths: Introduction to Quantum mechanics, Bolton & Lambourne: The Quantum World: wave mechanics)

  • Applies in this implementation:

    Ballentine has a modern approach that is used in this course. It may however be a bit more challenging to read than some of the other books mentioned. Just pay attention to the mathematical notation we use in the lectures and stick to that. The books may have a slightly more sloppy notation (forgetting operator hats etc.) but one can still learn the content from them. 

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    PHYS-C0210 Quantum Mechanics

  • Valid 01.08.2020-31.07.2022:

    Basics of electromagnetism, the ability to solve simple differential equations and integrals.

Registration for Courses
  • Valid 01.08.2020-31.07.2022:

    Registration via WebOodi.

  • Applies in this implementation:

    The course will be organized only online in Zoom. Use link


Details on the schedule
  • Applies in this implementation:

    Lecutres on Mondays and Wednesdays 10:15--12:00 and exercises on Fridays 10:15--12:00 for 26.10.--4.12.2020

    Mikko Möttönen will lecture the first three weeks followed by Tapio Ala-Nissilä for the last three weeks. Aravind Babu takes care of the exercises. This Zoom link is used for attending all these sessions.