From Classical Motion to Landau Levels: A Charged Particle in a Uniform Magnetic Field

Abstract

This thesis studies the motion of a charged particle in a uniform magnetic field, starting from the classical description and ending with the quantum mechanical Landau level picture. First, the classical trajectory is analyzed using the Lorentz force, showing that the particle moves in circular orbits with a characteristic cyclotron frequency. Then the problem is reformulated in terms of the Lagrangian and Hamiltonian formalisms, which provide a bridge to the quantum treatment. In the quantum case, the motion becomes quantized and leads to discrete energy levels known as 'Landau levels'. The thesis highlights the connection between the classical and quantum descriptions and explains the physical meaning of this quantization.