Self-adjoint extensions of Coulomb systems in 1, 2and 3 dimensions

摘要

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, pres ent a discussion of controversies in the literature, particularly the question of the permeability of the origin. Potentials given by fun damental solutions of Laplace equation are also briefly considered.