Pole structure of the Hamiltonian $ζ$-function for a singular potential

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dc.creatorFalomir, H.
dc.creatorPisani, P. A. G.
dc.creatorWipf, A.
dc.date2001-12-11
dc.date2002-05-13
dc.date.accessioned2026-07-07T10:54:13Z
dc.date.available2026-07-07T10:54:13Z
dc.descriptionWe study the pole structure of the $ζ$-function associated to the Hamiltonian $H$ of a quantum mechanical particle living in the half-line $\mathbf{R}^+$, subject to the singular potential $g x^{-2}+x^2$. We show that $H$ admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter $g$. The $ζ$-functions of these operators present poles which depend on $g$ and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.
dc.description12 pages, 1 figure, RevTeX. References added. Version to appear in Jour. Phys. A: Math. Gen
dc.identifierhttps://arxiv.org/abs/math-ph/0112019
dc.identifierhttp://arxiv.org/abs/math-ph/0112019
dc.identifierJ.Phys.A35:5427-5444,2002
dc.identifierdoi:10.1088/0305-4470/35/26/306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185733
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectFunctional Analysis
dc.subjectSpectral Theory
dc.subjectQuantum Physics
dc.subject81Q10, 34L05, 34L40
dc.titlePole structure of the Hamiltonian $ζ$-function for a singular potential
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