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: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2002
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/129682 |
| Aporte de: |
| 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. |
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