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Generalization of the Birman-Schwinger method for the number of bound states

Abstract : We generalize the Birman-Schwinger method, and derive a general upper bound on the number of bound states in the S wave for a spherically symmetric potential. This general bound includes, of course, the Bargmann bound, but also leads, for increasing (negative) potentials, to a Calogero-Cohn-type bound. Finally, we show that for a large class among these potentials, one can obtain further improvements.
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http://hal.in2p3.fr/in2p3-00022968
Contributor : Suzanne Robert <>
Submitted on : Tuesday, April 18, 2000 - 11:39:19 AM
Last modification on : Wednesday, September 16, 2020 - 4:07:23 PM

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  • HAL Id : in2p3-00022968, version 1

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K. Chadan, R. Kobayashi, M. Lassaut. Generalization of the Birman-Schwinger method for the number of bound states. Journal of Mathematical Physics, American Institute of Physics (AIP), 1999, 40, pp.1756-1763. ⟨in2p3-00022968⟩

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