Abstract
The study of the motion of a charged particle in a uniform magnetic field allows us to establish many elements of magnetism. After briefly recalling the results obtained in classical physics (Newtonian dynamics), we moved on to the quantum case. We introduced the notion of Landau levels for the eigenspaces of the Hamiltonian and discussed their degeneracy. We then discussed some particularly important physical effects associated with this quantization into Landau levels. In particular, we introduced the notion of edge state, which plays a central role in the physics of the quantum Hall effect, and illustrated it by describing an interferometry experiment between two electronic circuits, as well as a transposition of this concept to a gas of cold atoms confined in an optical lattice.
