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arXiv · 1211.5597

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

F. Caruso·J. A. Helayël-Neto·J. Martins·V. Oguri
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Abstract

The hydrogen atom in two dimensions, described by a Schr\"odinger 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 $-3,5 \times 10^{-3} eV \leq E \leq -9,0 \times 10^{-2} eV$, corresponding to a mean radius of the electron in the range $ (5.637 \pm 0.005) \times 10^{-8}$~cm $\leq \leq (48.87 \pm 0.03) \times 10^{-8}$~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.

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F. Caruso, J. A. Helayël-Neto, J. Martins, V. Oguri. 2012-11-22. Effects on the Non-Relativistic Dynamics of a Charged Particle Interacting with a Chern-Simons Potential. https://doi.org/10.1140/epjb%2Fe2013-40282-1

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