# NMAA05012U  Mathematical Physics (MatFys)

Volume 2018/2019
Education

BSc Programme in Physics
BSc Programme in Mathematics

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

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.

Introduktion til matematik (MatIntro) and Lineær Algebra (LinAlg) or similar. Analysis 0 (AN0) or Analysis 1 (An1) or similar will be an advantage.
5 hours of lectures and 4 hours of exercises per week for 9 weeks.
Credit
7,5 ECTS
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.
Aid
All aids allowed
Marking scale
Censorship form
No external censorship
One internal examiner
Re-exam

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.

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