Eur. Phys. J. B (2013) 86: 324
https://doi.org/10.1140/epjb/e2013-40282-1

Regular Article

Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

¹ Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, 22290-180, Urca, Rio de Janeiro, Brazil
² Instituto de Física Armando Dias Tavares, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524, 20550-900, Maracanã, Rio de Janeiro, Brazil

^a e-mail: francisco.caruso@gmail.com

Received: 4 April 2013
Received in final form: 17 May 2013
Published online: 15 July 2013

Abstract

The hydrogen atom in two dimensions, described by a Schrödinger equation with a Chern-Simons potential, is numerically solved. Both its wavefunctions and eigenvalues were determined for small values of the principal quantum number n. The only possible states correspond to l = 0. How the result depends on the topological mass of the photon is also discussed. In the case n = 1, the energy of the fundamental state, corresponding to different choice for the photon mass scale, are found to be comprehended in the interval −3.5 × 10^-3 eV ≤ E ≤ −9.0 × 10^-2 eV, corresponding to a mean radius of the electron in the range (5.637 ± 0.005) × 10^-8 cm ≤ ⟨r⟩ ≤ (48.87 ± 0.03) × 10^-8 cm. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction.