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
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Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/129682
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Sumario: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.