Charged Particle in Magnetic Field: Landau Levels

This lecture covers the behavior of a charged particle in a constant magnetic field, focusing on the generators of translations and Landau levels. The instructor explains the background electromagnetic field, the electric charge, and the formation of Landau levels. Non-relativistic limits and kinetic momentum are discussed, along with the challenges of finding generators of translation. The lecture also explores the ansatz method and the realization of spatial translations. The concept of translation invariance is highlighted, and the lecture delves into the Landau levels, discussing the many states within them and the impact of magnetic flux. Various examples and mathematical derivations are provided to illustrate the key concepts.