1211.5597 (F. Caruso et al.)

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

F. Caruso, J. A. Helayël-Neto, J. Martins, V. Oguri

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} \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.

View original: http://arxiv.org/abs/1211.5597