Quantized Kepler-Coulomb dynamical models on two-dimensional constant curvature spaces

TL;DR

This paper extends the quantization of Kepler-Coulomb models to two-dimensional constant curvature spaces, using the Sommerfeld polynomial method, with potential applications in nanostructure dynamics.

Contribution

It introduces a quantum-level formulation of Kepler-Coulomb models on curved surfaces, expanding previous work on oscillatory models in Riemannian spaces.

Findings

Quantization achieved using Sommerfeld polynomial method.

Models applicable to nanostructures like graphene and nanotubes.

Connections established with rigid body dynamics.

Abstract

The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on sphere and pseudosphere. Here we concentrate on Kepler-Coulomb potential models. We have used formulated in [6] the two-dimensional situation on the quantum level. The Sommerfeld polynomial method is used to perform the quantization of such problems. The quantization of two-dimensional problems may have something to do with the dynamics of graphens, fullerens and nanotubes. This problem is also nearly related to the so-called restricted problems of rigid body dynamic [1], [8].