Self-adjoint extensions of Coulomb systems in 1,2 and 3 dimensions
  We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in $R^n$, n = 1, 2, 3. We characterize their self-adjoint extensions and, in the unidimensional case, present a discussion of controversies in the literature, particularly the question of the permeability of the origin. Potentials given by fundamental solutions of Laplace equation are also briefly considered. 
Cesar R. de Oliveira, Alessandra A. Verri