2001/12/31 by H. Falomir, Pablo Pisani, P. A. G. Pisani +2 · 4 citations
Mathematics · Physics and Astronomy · #Geometry #Hamiltonian (control theory) #Irrational number #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Riemann zeta function #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.FA #math.MP #math.SP #msc:34L05 #msc:34L40 #msc:81Q10 #quant-ph
paper · pdf · doi:10.1088/0305-4470/35/26/306
published as J.Phys.A35:5427-5444,2002 · 12 pages, 1 figure, RevTeX. References added. Version to appear in Jour. Phys. A: Math. Gen
arxiv created 2002/05/13 · openalex publication_date 2002/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the pole structure of the ζ-function associated with the Hamiltonian H of a quantum mechanical particle living in the half-line ℝ + , subject to the singular potential gx −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.