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. https://resolver.caltech.edu/CaltechAUTHORS:20181120-133838721
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Abstract
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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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. | ||||||
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Issue or Number: | 7 | ||||||
DOI: | 10.1063/1.1664948 | ||||||
Record Number: | CaltechAUTHORS:20181120-133838721 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20181120-133838721 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 91075 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | George Porter | ||||||
Deposited On: | 20 Nov 2018 22:51 | ||||||
Last Modified: | 16 Nov 2021 03:38 |
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