Potenciais quânticos induzidos por geometria.

Abstract

The geometry has been extensively studied in recent years, mainly due to its many potential applications. Its role in gravity is well known by physicists as an example have a particle freely moving only under the influence of the gravitational field. Enough emphasis has been given to studies of quantum phenomena induced by geometry, for example, calculate the quantum potential. We follow this path in this dissertation. From the fundamental point of view, we introduce some basic concepts of Riemannian geometry, such as covariant derivative, parallel transport and curvature tensor. Thereafter, we show how to write the Schrodinger equation on a curved surface from the Dirac equation in curved space 2+1. Our results are compared to those from the Schrodinger equation obtained from a formalism that abuts quantum particles in an interface curve. Investigammos quantum particles on some surfaces, such as surfaces hyperbolic paraboloids, obtaining information about the region of greatest probability for the location of these particles, or specific surface area may occur where the containment of these qualitatively.