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

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 + x². We show that H admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter g. The...

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Autores principales: Falomir, Horacio Alberto, González Pisani, Pablo Andrés, Wipf, Andreas
Formato: Articulo
Lenguaje:Inglés
Publicado: 2002
Materias:
Ciencias Exactas
Física
Operator theory
Functional analytical methods
Quantum theory
Ordinary differential operators
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/129682
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-129682
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Física
Operator theory
Functional analytical methods
Quantum theory
Ordinary differential operators
spellingShingle Ciencias Exactas
Física
Operator theory
Functional analytical methods
Quantum theory
Ordinary differential operators
Falomir, Horacio Alberto
González Pisani, Pablo Andrés
Wipf, Andreas
Pole structure of the Hamiltonian ζ-function for a singular potential
topic_facet Ciencias Exactas
Física
Operator theory
Functional analytical methods
Quantum theory
Ordinary differential operators
description 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 + x². 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.
format Articulo
Articulo
author Falomir, Horacio Alberto
González Pisani, Pablo Andrés
Wipf, Andreas
author_facet Falomir, Horacio Alberto
González Pisani, Pablo Andrés
Wipf, Andreas
author_sort Falomir, Horacio Alberto
title Pole structure of the Hamiltonian ζ-function for a singular potential
title_short Pole structure of the Hamiltonian ζ-function for a singular potential
title_full Pole structure of the Hamiltonian ζ-function for a singular potential
title_fullStr Pole structure of the Hamiltonian ζ-function for a singular potential
title_full_unstemmed Pole structure of the Hamiltonian ζ-function for a singular potential
title_sort pole structure of the hamiltonian ζ-function for a singular potential
publishDate 2002
url http://sedici.unlp.edu.ar/handle/10915/129682
work_keys_str_mv AT falomirhoracioalberto polestructureofthehamiltonianzfunctionforasingularpotential
AT gonzalezpisanipabloandres polestructureofthehamiltonianzfunctionforasingularpotential
AT wipfandreas polestructureofthehamiltonianzfunctionforasingularpotential
bdutipo_str Repositorios
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