The interaction of a quantum charged particle with a classical magnetic field

This work aims to make an introduction to the study of a quantum system of a charged particle immersed in a constant magnetic field. First of all, this work starts by recovering some basic concepts of Quantum Mechanics: as Schrödinger equation and Heisenberg equation, time evolution of states, states and operators in position space. This review is a step of the work that complements the next one: the construction of the essential tools for the study of the interaction of a charged particle under the action of a constant magnetic field. Finally, we present the main objective of the paper, which is to show that the study of this interaction, in the Schrödinger wave quantum mechanics formalism, can be realized through Landau levels and the Aharonov–Bohm effect.

Keywords:
Fields and charged particles; landau levels, and the Aharonov–Bohm effect