The exciton ground state and excited state energies are obtained within the single band approximation for a model system of an infinitely long cylindrical wire. The effective Coulomb potential between the electron and the hole is studied as function of the wire radius and difference in dielectric permittivity inside and outside of the wire. Within the adiabatic approximation, we obtain "exact" numerical results for the effective exciton potential and the lowest exciton energy levels. The effective exciton potential is fitted to a tractable analytical expression that will facilitate further calculations.

No abstract

Recently it was proved that the Majumdar-Ghosh chain with the Hamiltonian has at least two ground states, in which the spins are arranged in nearest-neighbour singlet pairs. In this work it is shown that these two states are the only ground states. Besides, a rapidly converging variational method is given to determine the elementary excitations.