This project consist on the final Bachelor degree project in Physics of Angel Delgado Panadero in the university of Salamanca(USal).
In this study we will analize the movement of fermions in presence of a constant magnetic field, we will approach the problem from a classic frame, passing through the Landau quantization problem, to finally reach the spectre and eigenstates in the quantum relativistic problem, which we will refer as the problem of Dirac-Landau. All the results will be particularized to the constriction to (2+1)-dimensions and will be compared with the results obtained in the case of (3+1)-dimensions. Moreover, exploiting the freedom of choice of the gauge for the potencial vector to describe the magnetic field, we are going to obtain the wave function not only for the gauge of Landau, but also for the symmetrical gauge comparing both results. Finally, we will relate the results obtained in the plain constriction for studying phoenomenoes from the condensed matter such as the Quantum Hall Efect and the Graphene.
Key Words: Dirac-Landau, (2+1)-dimensions, Symmetrical gauge, Gauge of Landau, Quantum Hall Effect, Graphene