ar X iv : 0 70 8 . 08 66 v 1 [ qu an t - ph ] 7 A ug 2 00 7 Singular potentials in quantum mechanics and ambiguity in the self - adjoint Hamiltonian ∗

ar X iv : 0 70 8 . 08 66 v 2 [ qu an t - ph ] 2 6 O ct 2 00 7 Singular potentials in quantum mechanics and ambiguity in the self - adjoint Hamiltonian ∗

For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V (x) = g/x with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physica...

ar X iv : 0 80 8 . 10 23 v 1 [ qu an t - ph ] 7 A ug 2 00 8 CATEGORICAL QUANTUM MECHANICS

ar X iv : 0 80 6 . 27 64 v 1 [ m at h - ph ] 1 7 Ju n 20 08 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 Rn, 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 consid...

ar X iv : 0 90 5 . 09 74 v 1 [ m at h - ph ] 7 M ay 2 00 9 Symmetries and resonance sets for δ ′ - interactions July 20 , 2009

The symmetry properties of the family of δ ′-interactions with a resonant non-zero transparency resulting in non-separated states are discussed. It is shown that the connection matrix for these physically motivated interactions and the corresponding family of self-adjoint extensions can be constructed in a self-consistent way if the product δ ′ (x)ψ(x), where ψ(x) is a discontinuous wavefunctio...

ar X iv : 0 70 6 . 02 37 v 1 [ qu an t - ph ] 1 J un 2 00 7 Quantum Mechanics in Phase Space

In this paper, I am presenting the basics of the Wigner formulation of Quantum-Mechanics in a very simple language and write about few interpretational stuff raised around it.