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

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

2008-06-17

arxiv.org/abs/0806.2764v1

Physics

Mathematical Physics

23 pages; Annals of Physics (NY)

Scientific paper

10.1016/j.aop.2008.06.001

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.

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