Estudo sobre as interações atômicas e moleculares em configurações planares

Abstract

Different types of interaction potentials between charged particles that form atoms and molecules, limited to a planar region, are studied, among them: the usual Coulomb potential 1/r, the potential of the type ln(r), the Chern-Simons potential as well as the potentials composed of the first two (1/r and ln(r)) plus a simple harmonic external potential of frequency Ω capable of describing a model for a quantum dot. From them, the necessary calculations for the solution of the Schrödinger equation referring to different atoms and molecules are developed. All cases were numerically solved using the Numerov method, with which several wave functions and their respective energy eigenvalues were obtained. Such results aim to provide theoretical predictions capable of shedding light on what would be the effective form of interaction between charged particles in two dimensions, once they can be compared with future experimental data. In particular, we look in more detail at how these results can influence muon-catalyzed fusion, and we find promising estimates that suggest that this type of fusion can benefit if it can be performed in a planar configuration. It is expected that the conclusions obtained in this thesis can serve as a motivation for experimental physicists to search for different forms of interactions between particles when located in planar regions.