As a model of excitonic behavior the paper concerns itself with the one-electron states generated by a bare Coulomb potential-Ze2/r, plus an applied magnetic field H which is assumed intense. A quantity which reflects the entire one-electron level spectrum (epsilon) i and the corresponding wave functions (formula available in paper) is the canonical density matrix (formula available in paper) whose trace is the partition function Z(beta) .The inverse Laplace transform of C/(beta) yields the Dirac density matrix (zetz) (r,r,E), its diagonal element being the integrated local density of states. For free electrons in an intense field (formula available in paper) in three dimensions and in the presence of the Coulomb potential the Thomas-Fermi approximation replaces E by (formula available in paper). One can approximate, albeit somewhat crudely, the lowest energy state by finding the energy, E1 say, such that (integral) (formula available in paper). Such a procedure leads to a large error in E1 for H equals O but is expected to be a better approximation in an intense field. Applying the same approximation in two dimensions, with the magnetic field perpendicular to the plane of confinement assumed for the electrons, leads again to an estimate for the lowest one-electron state in an intense field. This motivates then a further study of this 2D case, in which the pure cylindrical symmetry of the 2D zero field case is preserved. Finally, in an Appendix, the bare Coulomb limit of a recent, self-consistent field, treatment by Lieb et al, of atoms in a hyperstrong field such that, in suitable units, H Z3 is set out.