NMAA05012U Mathematical physics (MatFys)
A. Representation theory. A1. Fourier transformation and the
translation group. A2. SO(3) and SU(2) and their Lie algebras. A3.
Tensor products and tensoring of representations.
B. Quantum mechanics. B1. The free Laplacean, momentum
representation (= spectral mapping), domain questions. B2. The
Schroedinger operator for the harmonic oscillator. B3. Rotationally
symmetric potentials and the hydrogen atom.
C. Differential forms on R^n. C1. Exterior product, closed forms,
exact forms, volume form and the *-operation. C2. Examples. F.ex.
Thermodynamics, Maxwell's equations, Hamiltonian formalism in
classical mechanics.
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
Skills:
- 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.
- Category
- Hours
- Exam
- 25
- Lectures
- 45
- Preparation
- 100
- Theory exercises
- 36
- Total
- 206
As
an exchange, guest and credit student - click here!
Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessmentThe students' performance will be evaluated on the basis of three assignments during the course, the last one being a mini project in week 9.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
- Final exam with two internal examiners given for a 30 minutes oral exam without preparation.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.
Course information
- Language
- English
- Course code
- NMAA05012U
- Credit
- 7,5 ECTS
- Level
- Bachelor
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- C
- Course capacity
- Ingen begrænsning
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Bergfinnur Durhuus (7-6677746a777775426f63766a306d7730666d)