Confinamento quântico em curvas planas

Abstract

The study of quantum confinement that takes into account aspects of differential geometry has attracted a lot of attention nowadays due to the possibility that those can offer tools for the development of quantum systems with control of physical-chemical properties via geometry, which is especially relevant for nanostructured materials. In this work we will explore the problem of confinement in curves immersed in R3, examining how the curvature and topology of the curve affect the physical properties of these systems. We developed a code in Python with differential geometry tools applied to curves, for solving the one-dimensional Schrödinger equation with potentials induced by geometry. We presented and discussed the numerical solutions for confinement on lines, circumferences, ellipses, catenaries, logarithmic spirals and meanders.