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Journal Articles Journal of Mathematical Physics Year : 1999

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

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K. Chadan
  • Function : Author
R. Kobayashi
  • Function : Author

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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Dates and versions

in2p3-00022968 , version 1 (18-04-2000)

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  • HAL Id : in2p3-00022968 , version 1

Cite

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

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