  The wave functions and the ground state energies for the bound states of four
different muonic and electronic molecules, governed by the Chern-Simons
potential in two spatial dimensions, are numerically obtained with the Numerov
method. The new results are compared with former planar configuration studies
that consider the attractive potential as being proportional to $\ln(\rho)$, as
well as with the three-dimensional analogs assuming a Coulomb potential.
