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:
Particle Physics - Theory
Acceso en línea:https://dx.doi.org/10.1063/1.531450
http://cds.cern.ch/record/290649
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author Chadan, K.
Kobayashi, R.
Martin, Andre
Stubbe, J.
author_facet Chadan, K.
Kobayashi, R.
Martin, Andre
Stubbe, J.
author_sort Chadan, K.
collection CERN
description 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.
id cern-290649
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1995
record_format invenio
spelling cern-2906492023-03-14T18:58:35Zdoi:10.1063/1.531450http://cds.cern.ch/record/290649engChadan, K.Kobayashi, R.Martin, AndreStubbe, J.Generalization of the Calogero-Cohn bound on the number of bound statesParticle Physics - TheoryIt 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.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 $p = 1/2$.hep-th/9511012CERN-TH-95-152-REVLPTHE-ORSAY-95-32-REVENSLAPP-A558-95-REVCERN-TH-95-152-REVENSLAPP-A-558LPTHE-95-32-REVoai:cds.cern.ch:2906491995-11-02
spellingShingle Particle Physics - Theory
Chadan, K.
Kobayashi, R.
Martin, Andre
Stubbe, J.
Generalization of the Calogero-Cohn bound on the number of bound states
title Generalization of the Calogero-Cohn bound on the number of bound states
title_full Generalization of the Calogero-Cohn bound on the number of bound states
title_fullStr Generalization of the Calogero-Cohn bound on the number of bound states
title_full_unstemmed Generalization of the Calogero-Cohn bound on the number of bound states
title_short Generalization of the Calogero-Cohn bound on the number of bound states
title_sort generalization of the calogero-cohn bound on the number of bound states
topic Particle Physics - Theory
url https://dx.doi.org/10.1063/1.531450
http://cds.cern.ch/record/290649
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AT kobayashir generalizationofthecalogerocohnboundonthenumberofboundstates
AT martinandre generalizationofthecalogerocohnboundonthenumberofboundstates
AT stubbej generalizationofthecalogerocohnboundonthenumberofboundstates

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