Charged Particle in Magnetic Field: Landau Levels

This lecture covers the behavior of a charged particle in a constant magnetic field, discussing Landau levels, the Aharonov-Bohm effect, and magnetic monopoles. The instructor explains the non-relativistic limit, gauge transformations, and spatial translations in the presence of the magnetic field. The lecture delves into the Hamiltonian, conjugate momenta, and canonical transformations. It also explores the challenges in finding generators for spatial translations and the projective realization of translations. The concept of gauge invariance and the classical motion of charged particles are also discussed, along with the quantum states in the presence of a magnetic field, leading to Landau levels.