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Generalization of the Calogero-Cohn bound on the number of bound states

It is shown that for the Calogero-Cohn type upper bounds on the number of bound states of a negative spherically symmetric potential V(r), in each angular momemtum state, that is, bounds containing only the integral \int^\infty_0 |V(r)|^{1/2}dr, the condition V'(r) \geq 0 is not necessary, and...

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Detalles Bibliográficos
Autores principales: Chadan, K., Kobayashi, R., Martin, Andre, Stubbe, J.
Lenguaje:eng
Publicado: 1995
Materias:
Acceso en línea:https://dx.doi.org/10.1063/1.531450
http://cds.cern.ch/record/290649
Descripción
Sumario:It is shown that for the Calogero-Cohn type upper bounds on the number of bound states of a negative spherically symmetric potential V(r), in each angular momemtum state, that is, bounds containing only the integral \int^\infty_0 |V(r)|^{1/2}dr, the condition V'(r) \geq 0 is not necessary, and can be replaced by the less stringent condition (d/dr)[r^{1-2p}(-V)^{1-p}] \leq 0, 1/2 \leq p < 1, which allows oscillations in the potential. The constants in the bounds are accordingly modified, depend on p and \ell, and tend to the standard value for p = 1/2.