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 ∗

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 ∗

For a class of singular potentials, including the Coulomb potential and V (x) = g/x with the coefficient g in a certain range, 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 physical consequences depend seriously on the selfadjoint version chosen. The talk discusses ...

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

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 81 0 . 52 70 v 1 [ he p - ph ] 2 9 O ct 2 00 8 PT Symmetry and Hermithean Hamiltonian in the Local Supercritical Pomeron Model

The local reggeon field theory is studied perturbatively taking advantage of the PT symmetry in the Hamiltonian formulation. In the lowest non trivial order we show that the pomeron interactions renormalize the slope. In the same order we find a non local pair potential acting between pomerons, which has a singular structure. However the analysis of the scattering operator shows that at small c...