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 permeabilit...

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Bibliographic Details
Published in:Annals of physics 2009-02, Vol.324 (2), p.251-266
Main Authors: de Oliveira, César R., Verri, Alessandra A.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Coulomb systems
HAMILTONIANS
LAPLACE EQUATION
MATHEMATICAL SOLUTIONS
Origin permeability
PERMEABILITY
POTENTIALS
RIEMANN SPACE
Self-adjoint extensions
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Summary: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.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2008.06.001