Evolution in time of an N-atom system. II. Calculation of the eigenstates

We calculate the energy eigenvalues and eigenstates corresponding to coherent single and multiple excitations of a number of different arrays of N identical two-level atoms (TLA's) or qubits, including polygons, ``diamond{''} structures, polygon multilayers, icosahedra, and dodecahedra. We assume only that the coupling occurs via an exchange interaction which depends on the separation between the atoms. We include the interactions between all pairs of atoms, and our results are valid for arbitrary separations relative to the radiation wavelength.