LIMA, C. A. R.; http://lattes.cnpq.br/5804079023507059; LIMA, Cícero Alécio Rodrigues de.
Resumen:
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.