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On the Growth of the Number of Bound States with Increase in Potential Strength

Simon, Barry (1969) On the Growth of the Number of Bound States with Increase in Potential Strength. Journal of Mathematical Physics, 10 (7). pp. 1123-1126. ISSN 0022-2488. doi:10.1063/1.1664948.

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For a wide class of potentials, it is shown that N(λ), the number of bound states (including multiplicity) of −Δ + λV, obeys the conditions Aλ^(3/2) < N(λ) < Bλ^(3/2) for λ sufficiently large. A and B are positive finite numbers. In the centrally symmetric cases, a related growth condition on l_(max)(λ), the largest l channel with bound states, is also obtained, namely, aλ^(1/2) < l_(max)(λ) < bλ^(1/2). Finally, we discuss analogous results for a larger class of central potentials and for the many‐body case.

Item Type:Article
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Simon, Barry0000-0003-2561-8539
Additional Information:© 1969 The American Institute of Physics. (Received 21 November 1968) This research partially sponsored under Air Force Research and Development Command contract AF49(638)1545. It is a pleasure to thank Professor V. Bargmann and Professor A. S. Wightman for their interest and perceptive comments.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)AF 49(638)1545
NSF Graduate Research FellowshipUNSPECIFIED
Issue or Number:7
Record Number:CaltechAUTHORS:20181120-133838721
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91075
Deposited By: George Porter
Deposited On:20 Nov 2018 22:51
Last Modified:16 Nov 2021 03:38

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