Estudo do efeito da rotação e campos eletromagnéticos na mecânica quântica do elétron e suas implicações nas propriedades ópticas

Abstract

In this thesis, we study quantum mechanics in non-inertial reference frames in two different scenarios. First, we study the effects of rotation in the spin-1/2 non-relativistic Aharonov-Bohm problem for bound states. We use a technique based on the self-adjoint extension method and determine an expression for the energies of the bound states. Including the spin element in the Hamiltonian guarantees bound state solutions. We perform a numerical analysis of the energies and verify that both the rotation and the spin degrees of freedom affect the energies of the particle. The main effect we observe in this analysis is a cut-off value manifested in the AB flux parameter, which limits the values of the positive and negative energies. We then consider the effects of rotation on the nonrelativistic quantum motion of a charged particle confined to a 2D ring in the presence of the AB effect and a uniform magnetic field. We first formulate the Schr¨odinger equation with minimal coupling, including the rotating frame gauge field and the electromagnetic field’s potential vector. By solving the equation of motion, we determine the eigenvalues and eigenfunctions of the particle. We analyze the probability distribution as a function of varying rotation parameter values and observe a noticeable shift in the distribution. This shift indicates a higher probability of locating the electron at the ring’s edges. We then investigate the effects of rotation on the system’s linear and nonlinear optical properties. In particular, we study the linear, nonlinear, and total refractive index changes and the optical absorption coefficients. We demonstrate significant rotation effects on energy levels and optical properties through numerical analysis. Our results indicate that, for the physical parameters considered, the effect of rotation on the optical properties becomes prominent at values of the order of a few terahertz.