NMAA05012U Mathematical physics (MatFys)

Volume 2013/2014
Education
Bacheloruddanenlsen i de fysiske fag
Content


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.
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.
MatIntro and LinAlg or similar. Analysis 0 or Analysis 1 will be an advantage.
5 hours of lectures and 4 hours of exercises per week for 9 weeks.
  • Category
  • Hours
  • Exam
  • 25
  • Lectures
  • 45
  • Preparation
  • 100
  • Theory exercises
  • 36
  • Total
  • 206
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 is 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.