Effects on the Non-Relativistic Dynamics of a Charged Particle Interacting with a Chern-Simons Potential

Abstract

The hydrogen atom in two dimensions, described by a Schrödinger equation with a Chern-Simons potential, is numerically solved. Both its wave functions 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 $-3,5\times 10^{-3}eV\le E\le -9,0\times 10^{-2}eV$, corresponding to a mean radius of the electron in the range $(5.637\pm 0.005)\times 10^{-8}$~cm $\le <r>\le (48.87\pm 0.03)\times 10^{-8}$~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.

6 pages, 5 figures

References in corpus (3)

• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Axion topological field theory of topological superconductors

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• Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory
• Using torsion to manipulate spin currents
• Non-relativistic solutions for three-body molecules within a Chern-Simons model
• Solving two-dimensional non-relativistic electronic and muonic atoms governed by Chern-Simon potential