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Coupling Constant Thresholds in Nonrelativistic Quantum Mechanics. I. Short-Range Two-Body Case

Klaus, M. and Simon, Barry (1980) Coupling Constant Thresholds in Nonrelativistic Quantum Mechanics. I. Short-Range Two-Body Case. Annals of Physics, 130 (2). pp. 251-281. ISSN 0003-4916. doi:10.1016/0003-4916(80)90338-3.

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Consider −Δ + λV with V short range at a value λ_0 where some eigenvalue e(λ) → 0 as λ ↓ λ_0. We analyze two questions: (i) What is the leading order of e(λ), i.e., for what α does e(λ) ∼ c(λ − λ_0)^α? (ii) Is e(λ) analytic at λ = λ_0 and, if not, what is the natural expansion parameter? The results are highly dimension dependent.

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Simon, Barry0000-0003-2561-8539
Additional Information:© 1980 Published by Elsevier. Received April 4, 1980; revised May 16, 1980. Research supported by Swiss National Science Foundation. Research supported by USNSF Grant MCS-78-01885. We should like to thank J. Morgan III and R. Newton for valuable discussions. One of us (B.S.) would like to thank the Technion Physics Department for its hospitality during the completion of this work.
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Swiss National Science Foundation (SNSF)UNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20180521-150501792
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Official Citation:M. Klaus, Barry Simon, Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case, Annals of Physics, Volume 130, Issue 2, 1980, Pages 251-281, ISSN 0003-4916, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86522
Deposited By: George Porter
Deposited On:21 May 2018 22:29
Last Modified:15 Nov 2021 20:39

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