ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
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 momentum state, that is, bounds containing only the integral ∫∞0||V(r)||1/2 dr, the condition V′(r)≥0 is not necessary, and can be replaced by the less stringent condition (d/dr)[r1−2p(−V)1−p]≤0, 1/2≤p〈1, which allows oscillations in the potential. The constants in the bounds are accordingly modified, depend on p and l, and tend to the standard value for p=1/2. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.531450
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