On Lennard-Jones-type potentials on the half-line
In this paper we study a particle under the influence of a Lennard-Jones potential moving in a simple quantum wire modelled by the positive half-line. Despite its physical significance, this potential is only rarely studied in the literature and due to its singularity at the origin it cannot be cons...
Gespeichert in:
| Veröffentlicht in: | Archiv der Mathematik 2019-01, Vol.112 (1), p.101-111 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 111 |
|---|---|
| container_issue | 1 |
| container_start_page | 101 |
| container_title | Archiv der Mathematik |
| container_volume | 112 |
| creator | Gregorio, Federica Kerner, Joachim |
| description | In this paper we study a particle under the influence of a Lennard-Jones potential moving in a simple quantum wire modelled by the positive half-line. Despite its physical significance, this potential is only rarely studied in the literature and due to its singularity at the origin it cannot be considered as a standard perturbation of the one-dimensional Laplacian. It is therefore our aim to provide a thorough description of the full Hamiltonian in one dimension via the construction of a suitable quadratic form. Our results include a discussion of spectral and scattering properties which finally allows us to generalise some results from Robinson (Ann Inst H Poincaré Sect A (N.S.) 21(3):185–215,
1974
) as well as Radin and Simon (J Differ Equ 29(2):289–296,
1978
). |
| doi_str_mv | 10.1007/s00013-018-1243-4 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2168703976</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2168703976</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-8bb41168d568f31de3d3d255c65ec0cce5f837c69010a10948dc2ed80ebec1883</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhoMoWKs_wNuC5-hMsh-zRyl-stCLgrewTWZtS82uyfbQf2_KCp48Dcw87zvwCHGNcIsA1V0EANQSkCSqXMv8RMwwVyCp1nQqZumsJVH9cS4uYtwmWFFVzwQufdaw921w8rX3HOV4GDgb-pH9uGl3Met9Nq45W7e7Tu42ni_FWZf2fPU75-L98eFt8Syb5dPL4r6RVmM5SlqtcsSSXFFSp9GxdtqporBlwRas5aIjXdmyBoQWoc7JWcWOgFdskUjPxc3UO4T-e89xNNt-H3x6aVTqrUDXVZkonCgb-hgDd2YIm682HAyCOZoxkxmTzJijGZOnjJoyMbH-k8Nf8_-hHwY0ZHk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2168703976</pqid></control><display><type>article</type><title>On Lennard-Jones-type potentials on the half-line</title><source>Springer Nature - Complete Springer Journals</source><creator>Gregorio, Federica ; Kerner, Joachim</creator><creatorcontrib>Gregorio, Federica ; Kerner, Joachim</creatorcontrib><description>In this paper we study a particle under the influence of a Lennard-Jones potential moving in a simple quantum wire modelled by the positive half-line. Despite its physical significance, this potential is only rarely studied in the literature and due to its singularity at the origin it cannot be considered as a standard perturbation of the one-dimensional Laplacian. It is therefore our aim to provide a thorough description of the full Hamiltonian in one dimension via the construction of a suitable quadratic form. Our results include a discussion of spectral and scattering properties which finally allows us to generalise some results from Robinson (Ann Inst H Poincaré Sect A (N.S.) 21(3):185–215,
1974
) as well as Radin and Simon (J Differ Equ 29(2):289–296,
1978
).</description><identifier>ISSN: 0003-889X</identifier><identifier>EISSN: 1420-8938</identifier><identifier>DOI: 10.1007/s00013-018-1243-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Lennard-Jones potential ; Mathematics ; Mathematics and Statistics ; Quadratic forms ; Quantum wires</subject><ispartof>Archiv der Mathematik, 2019-01, Vol.112 (1), p.101-111</ispartof><rights>Springer Nature Switzerland AG 2018</rights><rights>Copyright Springer Science & Business Media 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-8bb41168d568f31de3d3d255c65ec0cce5f837c69010a10948dc2ed80ebec1883</citedby><cites>FETCH-LOGICAL-c316t-8bb41168d568f31de3d3d255c65ec0cce5f837c69010a10948dc2ed80ebec1883</cites><orcidid>0000-0003-0638-4183</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00013-018-1243-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00013-018-1243-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Gregorio, Federica</creatorcontrib><creatorcontrib>Kerner, Joachim</creatorcontrib><title>On Lennard-Jones-type potentials on the half-line</title><title>Archiv der Mathematik</title><addtitle>Arch. Math</addtitle><description>In this paper we study a particle under the influence of a Lennard-Jones potential moving in a simple quantum wire modelled by the positive half-line. Despite its physical significance, this potential is only rarely studied in the literature and due to its singularity at the origin it cannot be considered as a standard perturbation of the one-dimensional Laplacian. It is therefore our aim to provide a thorough description of the full Hamiltonian in one dimension via the construction of a suitable quadratic form. Our results include a discussion of spectral and scattering properties which finally allows us to generalise some results from Robinson (Ann Inst H Poincaré Sect A (N.S.) 21(3):185–215,
1974
) as well as Radin and Simon (J Differ Equ 29(2):289–296,
1978
).</description><subject>Lennard-Jones potential</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Quadratic forms</subject><subject>Quantum wires</subject><issn>0003-889X</issn><issn>1420-8938</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wNuC5-hMsh-zRyl-stCLgrewTWZtS82uyfbQf2_KCp48Dcw87zvwCHGNcIsA1V0EANQSkCSqXMv8RMwwVyCp1nQqZumsJVH9cS4uYtwmWFFVzwQufdaw921w8rX3HOV4GDgb-pH9uGl3Met9Nq45W7e7Tu42ni_FWZf2fPU75-L98eFt8Syb5dPL4r6RVmM5SlqtcsSSXFFSp9GxdtqporBlwRas5aIjXdmyBoQWoc7JWcWOgFdskUjPxc3UO4T-e89xNNt-H3x6aVTqrUDXVZkonCgb-hgDd2YIm682HAyCOZoxkxmTzJijGZOnjJoyMbH-k8Nf8_-hHwY0ZHk</recordid><startdate>20190101</startdate><enddate>20190101</enddate><creator>Gregorio, Federica</creator><creator>Kerner, Joachim</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-0638-4183</orcidid></search><sort><creationdate>20190101</creationdate><title>On Lennard-Jones-type potentials on the half-line</title><author>Gregorio, Federica ; Kerner, Joachim</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-8bb41168d568f31de3d3d255c65ec0cce5f837c69010a10948dc2ed80ebec1883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Lennard-Jones potential</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Quadratic forms</topic><topic>Quantum wires</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gregorio, Federica</creatorcontrib><creatorcontrib>Kerner, Joachim</creatorcontrib><collection>CrossRef</collection><jtitle>Archiv der Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gregorio, Federica</au><au>Kerner, Joachim</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Lennard-Jones-type potentials on the half-line</atitle><jtitle>Archiv der Mathematik</jtitle><stitle>Arch. Math</stitle><date>2019-01-01</date><risdate>2019</risdate><volume>112</volume><issue>1</issue><spage>101</spage><epage>111</epage><pages>101-111</pages><issn>0003-889X</issn><eissn>1420-8938</eissn><abstract>In this paper we study a particle under the influence of a Lennard-Jones potential moving in a simple quantum wire modelled by the positive half-line. Despite its physical significance, this potential is only rarely studied in the literature and due to its singularity at the origin it cannot be considered as a standard perturbation of the one-dimensional Laplacian. It is therefore our aim to provide a thorough description of the full Hamiltonian in one dimension via the construction of a suitable quadratic form. Our results include a discussion of spectral and scattering properties which finally allows us to generalise some results from Robinson (Ann Inst H Poincaré Sect A (N.S.) 21(3):185–215,
1974
) as well as Radin and Simon (J Differ Equ 29(2):289–296,
1978
).</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00013-018-1243-4</doi><tpages>11</tpages><orcidid>https://orcid.org/0000-0003-0638-4183</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-889X |
| ispartof | Archiv der Mathematik, 2019-01, Vol.112 (1), p.101-111 |
| issn | 0003-889X 1420-8938 |
| language | eng |
| recordid | cdi_proquest_journals_2168703976 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Lennard-Jones potential Mathematics Mathematics and Statistics Quadratic forms Quantum wires |
| title | On Lennard-Jones-type potentials on the half-line |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-11T16%3A01%3A42IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20Lennard-Jones-type%20potentials%20on%20the%20half-line&rft.jtitle=Archiv%20der%20Mathematik&rft.au=Gregorio,%20Federica&rft.date=2019-01-01&rft.volume=112&rft.issue=1&rft.spage=101&rft.epage=111&rft.pages=101-111&rft.issn=0003-889X&rft.eissn=1420-8938&rft_id=info:doi/10.1007/s00013-018-1243-4&rft_dat=%3Cproquest_cross%3E2168703976%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2168703976&rft_id=info:pmid/&rfr_iscdi=true |