Related papers: Quantum particle motion on the surface of a helicoid in the presence of harmonic oscillator

Quantum particle motion on the surface of a helicoid in the presence of harmonic oscillator

URL: http://arxiv.org/abs/2005.01210v1
Date: Sun, 3 May 2020 23:47:11 GMT
Title: Quantum particle motion on the surface of a helicoid in the presence of harmonic oscillator
Authors: Marcos C. R. Ribeiro Jr., M\'arcio M. Cunha, Cleverson Filgueiras, Edilberto O. Silva
Abstract summary: We study the consequences of a helicoidal geometry in the Schr"odinger equation dealing with an anisotropic mass tensor. We determine the eigenfunctions in terms of Confluent Heun Functions and compute the respective energy levels.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The geometric potential in quantum mechanics has been attracted attention recently, providing a formalism to investigate the influence of curvature in the context of low-dimensional systems. In this paper, we study the consequences of a helicoidal geometry in the Schr\"{o}dinger equation dealing with an anisotropic mass tensor. In particular, we solve the problem of an harmonic oscillator in this scenario. We determine the eigenfunctions in terms of Confluent Heun Functions and compute the respective energy levels. The system exhibit several different behaviors, depending on the adjustment on the mass components.

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