Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Mathematical physics (MatFys)

Practical information
Study year 2016/2017
Block 2
Programme level Bachelor
Course responsibles
  • Bergfinnur Durhuus (7-6677746a777775426f63766a306d7730666d)
  • Jan Philip Solovej (7-75716e7178676c426f63766a306d7730666d)
Phone+45 35 32 07 35, office 04.4.06
  • Department of Mathematical Sciences
Course number: NMAA05012U

Course content

A. Classical mechanics: A1. Newtonian mechanics. A2. Calculus of variations and Lagrangian mechanics, including Noether's theorem. A3. Legendre-Fenchel transform and Hamiltonian mechanics, including Liouville's theorem.

B. Quantum mechanics: B1. Hilbert space theory. B2. Operators on Hilbert space, including basic spectral theory. B3. The quantum mechanical formalism, including the Schrödinger representation, the momentum representation, and Fourier transformation. B4. The free particle, the harmonic oscillator and the hydrogen atom.

Learning outcome

At the end of the course the students are expected to have acquired the following knowledge and associated tool box:

  • the mathematical formulation of clasical mechanics
  • the mathematical formulation of quantum mechanics
  • symmetries and transformations, e.g., the Galillei transformation
  • the fundamental theorems on Hilbert spaces
  • properties of simple bounded and unbounded operators
  • the free Laplace operator and elementary properties of its spectral theory



  • be able to work rigorously with problems from classical mechanics
  • be able to work rigorously with problems from quantum mechanics
  • be able to determine the spectrum of simple bounded and unbounded operators with discrete spectrum
  • be able to rigorously analyze the quantum harmonic oscillator and/or the hydrogen atom


Competences: The course aims at training the students in representing, modelling and handling physical problems by mathematical concepts and techniques.

Recommended prerequisites

Introduktion til matematik (MatIntro) and Lineær Algebra (LinAlg) or similar. Analysis 0 (AN0) or Analysis 1 (An1) will be an advantage.

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BSc Programme in Physics

BSc programme in Mathematics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


1 block


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Teaching and learning methods

5 hours of lectures and 4 hours of exercises per week for 9 weeks.


Ingen begrænsning




Category Hours
Lectures 45
Preparation 100
Exam 25
Theory exercises 36
English 206


Type of assessment

Continuous assessment
The students' performance will be evaluated on the basis of three assignments during the course, the last one being a mini project in week 9. When calculating the final mark, the three assignments are weighted equally.


All aids allowed

Marking scale

7-point grading scale

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.

Censorship form

No external censorship
One internal examiner


Final exam with two internal examiners: a 30 minutes oral exam without preparation or aids.

Mere information om kurset
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