NMAA05012U Mathematical Physics (MatFys)
BSc Programme in Physics
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.
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.
- Theory exercises
- 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. When calculating the final mark, the three assignments are weighted equally.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
Final exam with two internal examiners: a 30 minutes oral exam without preparation or aids.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.