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

Abstract

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.

arXiv comment23 pages; Annals of Physics (NY)

References in corpus (2)

• The functional-analytic versus the functional-integral approach to quantum Hamiltonians: The one-dimensional hydrogen atom.
• Dimensionalities of Weak Solutions in Hydrogenic Systems

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