The Breit-Wigner series for noncompactly supported potentials on the line
We propose a conjecture stating that for resonances, $\lambda_j$, of a noncompactly supported potential, the series $\sum_j \operatorname{Im} \lambda_j/|\lambda_j|^2$ diverges. This series appears in the Breit-Wigner approximation for a compactly supported potential, in which case it converges. We p...
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| creator | Backus, Aidan |
| description | We propose a conjecture stating that for resonances, $\lambda_j$, of a
noncompactly supported potential, the series $\sum_j \operatorname{Im}
\lambda_j/|\lambda_j|^2$ diverges. This series appears in the Breit-Wigner
approximation for a compactly supported potential, in which case it converges.
We provide heuristic motivation for this conjecture and prove it in several
cases. |
| doi_str_mv | 10.48550/arxiv.2005.13765 |
| format | Article |
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noncompactly supported potential, the series $\sum_j \operatorname{Im}
\lambda_j/|\lambda_j|^2$ diverges. This series appears in the Breit-Wigner
approximation for a compactly supported potential, in which case it converges.
We provide heuristic motivation for this conjecture and prove it in several
cases.</description><identifier>DOI: 10.48550/arxiv.2005.13765</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs ; Mathematics - Complex Variables ; Mathematics - Mathematical Physics ; Mathematics - Spectral Theory ; Physics - Mathematical Physics</subject><creationdate>2020-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2005.13765$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2005.13765$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Backus, Aidan</creatorcontrib><title>The Breit-Wigner series for noncompactly supported potentials on the line</title><description>We propose a conjecture stating that for resonances, $\lambda_j$, of a
noncompactly supported potential, the series $\sum_j \operatorname{Im}
\lambda_j/|\lambda_j|^2$ diverges. This series appears in the Breit-Wigner
approximation for a compactly supported potential, in which case it converges.
We provide heuristic motivation for this conjecture and prove it in several
cases.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Complex Variables</subject><subject>Mathematics - Mathematical Physics</subject><subject>Mathematics - Spectral Theory</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz81KxDAYheFsXMjoBbgyN9CaNH_tUgd_BgbcFFyWr8kXDXSSkEZx7t5xdHXgLF54CLnhrJW9UuwOynf4ajvGVMuF0eqS7MYPpA8FQ23ewnvEQlcsAVfqU6ExRZsOGWxdjnT9zDmVio7mVDHWAMtKU6T1FFhCxCty4U8XXv_vhoxPj-P2pdm_Pu-29_sGtFGNVBqUhAFnVMNsPM6WW88VN1L1okejHQh0zgnbA-_AIzMc9QAGhrmTndiQ27_s2TLlEg5QjtOvaTqbxA9x1kg8</recordid><startdate>20200527</startdate><enddate>20200527</enddate><creator>Backus, Aidan</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20200527</creationdate><title>The Breit-Wigner series for noncompactly supported potentials on the line</title><author>Backus, Aidan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a675-456a54a9ebe59b7febc1cf151745838e76da3eddd3c8a12afe071e69a7a9b2423</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Complex Variables</topic><topic>Mathematics - Mathematical Physics</topic><topic>Mathematics - Spectral Theory</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Backus, Aidan</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Backus, Aidan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Breit-Wigner series for noncompactly supported potentials on the line</atitle><date>2020-05-27</date><risdate>2020</risdate><abstract>We propose a conjecture stating that for resonances, $\lambda_j$, of a
noncompactly supported potential, the series $\sum_j \operatorname{Im}
\lambda_j/|\lambda_j|^2$ diverges. This series appears in the Breit-Wigner
approximation for a compactly supported potential, in which case it converges.
We provide heuristic motivation for this conjecture and prove it in several
cases.</abstract><doi>10.48550/arxiv.2005.13765</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs Mathematics - Complex Variables Mathematics - Mathematical Physics Mathematics - Spectral Theory Physics - Mathematical Physics |
| title | The Breit-Wigner series for noncompactly supported potentials on the line |
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