Pole structure of the Hamiltonian zeta function for a singular potential

H. FALOMIR, P.A.G. PISANI AND A. WIPF

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

IOP Publishing

Año: 2002 vol. A35 p. 5427 - 5444

0305-4470

We study the pole structure of the zeta-function associated to the Hamiltonian H of a quantum mechanical particle living in the half-line 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 zeta-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.