In this work we study the Landau levels in the presence of topological defects.We analyze the behavior of electrons moving in a magnetic field in the presence of a continuous distribution of disclinations, a magnetic screw dislocation and a dispiration. We focus on the influence of these topological defects on the spectrum of the electron (or hole) in the magnetic field in the framework of the geometric theory of defects in solids of Katanaev-Volovich. The presence of the defect breaks the degeneracy of the Landau levels in different ways depending on the defect. Exact expressions for energies and eigenfunctions are found for all cases. Using KaluzaKlein theory we solve the Landau level problem for a dispiration and compare the results with the ones obtained in the previous cases.

We study the behavior of non-relativistic quantum particles interacting with different potentials in the space-times generated by a cosmic string and a global monopole.We find the energy spectra in the presence of these topological defects and show how they differ from their free-space-time values.

We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a point-like global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the energy levels of the atom. We investigate how the geometric and topological features of these spacetimes leads to shifts in the energy levels as compared with the flat Minkowski spacetime.Comment: 17 pages, LATEX fil

Scalar quantum particles are considered in the Kerr–Newman, Gödel and Friedmann–Robertson–Walker spacetimes with a cosmic string passing through them. The solutions of the Klein–Gordon equation in these backgrounds are obtained and some of their consequences are discussed, with emphasis on the role played by the presence of the cosmic string.

We investigate the quantum scattering of an electron by a topological defect called dispiration, with an externally applied magnetic field along its axis. The Aharonov–Bohm effect for bound states is analyzed and it is demonstrated that the wave function and the energy spectra associated with the particle depend on the features of the dispiration as well as on the magnetic flux. We also calculate Berry's phase associated to the dynamics of electrons in this background.