Self-adjoint extensions of Coulomb systems in 1,2 and 3 dimensions
arXiv:0806.2764 · doi:10.1016/j.aop.2008.06.001
Abstract
We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in , 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.
23 pages; Annals of Physics (NY)