Estudo de geometria diferencial de superfície com aplicações para construção de mecânica quântica de partícula em coordenadas curvilíneas e no espaço curvo

Abstract

The aim of this work is to study the canonical quantization procedure of a particle in a Riemann space, as well as on a surface embedded in Euclidean space. To this aim, we rewrite quantum mechanics of a particle in Euclidean space in curvilinear coordinates. This allows us to formulate certain quantization procedure in a Riemann space. The resulting picture is compared with three quantization proposals known in the literature.