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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. https://resolver.caltech.edu/CaltechAUTHORS:20180521-150501792

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0003-4916(80)90338-3DOIArticle
ORCID:
AuthorORCID
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.
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)UNSPECIFIED
NSFMCS-78-01885
Issue or Number:2
DOI:10.1016/0003-4916(80)90338-3
Record Number:CaltechAUTHORS:20180521-150501792
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180521-150501792
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, https://doi.org/10.1016/0003-4916(80)90338-3. (http://www.sciencedirect.com/science/article/pii/0003491680903383)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86522
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:21 May 2018 22:29
Last Modified:15 Nov 2021 20:39

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