The relativistic Scott correction for atoms and molecules
Comm. Pure Appl. Math. 63 (2010), no. 1, 39--118 We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy, established in [Sore...
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| creator | Solovej, Jan Philip Sørensen, Thomas Østergaard Spitzer, Wolfgang L |
| description | Comm. Pure Appl. Math. 63 (2010), no. 1, 39--118 We prove the first correction to the leading Thomas-Fermi energy for the
ground state energy of atoms and molecules in a model where the kinetic energy
of the electrons is treated relativistically. The leading Thomas-Fermi energy,
established in [Sorensen], as well as the correction given here are of
semi-classical nature. Our result on atoms and molecules is proved from a
general semi-classical estimate for relativistic operators with potentials with
Coulomb-like singularities. This semi-classical estimate is obtained using the
coherent state calculus introduced in [Solovej-Spitzer]. The paper contains a
unified treatment of the relativistic as well as the non-relativistic case. |
| doi_str_mv | 10.48550/arxiv.0808.2163 |
| format | Article |
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ground state energy of atoms and molecules in a model where the kinetic energy
of the electrons is treated relativistically. The leading Thomas-Fermi energy,
established in [Sorensen], as well as the correction given here are of
semi-classical nature. Our result on atoms and molecules is proved from a
general semi-classical estimate for relativistic operators with potentials with
Coulomb-like singularities. This semi-classical estimate is obtained using the
coherent state calculus introduced in [Solovej-Spitzer]. The paper contains a
unified treatment of the relativistic as well as the non-relativistic case.</description><identifier>DOI: 10.48550/arxiv.0808.2163</identifier><language>eng</language><subject>Mathematics - Mathematical Physics ; Mathematics - Spectral Theory ; Physics - Mathematical Physics</subject><creationdate>2008-08</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/0808.2163$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.0808.2163$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Solovej, Jan Philip</creatorcontrib><creatorcontrib>Sørensen, Thomas Østergaard</creatorcontrib><creatorcontrib>Spitzer, Wolfgang L</creatorcontrib><title>The relativistic Scott correction for atoms and molecules</title><description>Comm. Pure Appl. Math. 63 (2010), no. 1, 39--118 We prove the first correction to the leading Thomas-Fermi energy for the
ground state energy of atoms and molecules in a model where the kinetic energy
of the electrons is treated relativistically. The leading Thomas-Fermi energy,
established in [Sorensen], as well as the correction given here are of
semi-classical nature. Our result on atoms and molecules is proved from a
general semi-classical estimate for relativistic operators with potentials with
Coulomb-like singularities. This semi-classical estimate is obtained using the
coherent state calculus introduced in [Solovej-Spitzer]. The paper contains a
unified treatment of the relativistic as well as the non-relativistic case.</description><subject>Mathematics - Mathematical Physics</subject><subject>Mathematics - Spectral Theory</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7tqw0AQRbdJYZz0rsL-gJTV7EsqjUlig8GF1YthNCILktesNib5ez-S6nT33CPEqlKlqa1Vb5h-wqVUtapLqJxeiKb9Ypl4xBwuYc6B5JFizpJiSkw5xJMcYpKY4zRLPPVyiiPT98jzs3gacJz55Z9L0X68t5ttsT987jbrfYHO6gJRIfHNBwbIgjNGDxaVd4Nn6rUB1SgH3noA5xsGW4HpwTRcUQ299XopXv9mH9e7cwoTpt_untDdE_QVYmA_wQ</recordid><startdate>20080815</startdate><enddate>20080815</enddate><creator>Solovej, Jan Philip</creator><creator>Sørensen, Thomas Østergaard</creator><creator>Spitzer, Wolfgang L</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20080815</creationdate><title>The relativistic Scott correction for atoms and molecules</title><author>Solovej, Jan Philip ; Sørensen, Thomas Østergaard ; Spitzer, Wolfgang L</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a653-aa0ace808242c526443f5a076f7ecd3420906275722679e25124d249e1c82d573</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Mathematics - Mathematical Physics</topic><topic>Mathematics - Spectral Theory</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Solovej, Jan Philip</creatorcontrib><creatorcontrib>Sørensen, Thomas Østergaard</creatorcontrib><creatorcontrib>Spitzer, Wolfgang L</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Solovej, Jan Philip</au><au>Sørensen, Thomas Østergaard</au><au>Spitzer, Wolfgang L</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The relativistic Scott correction for atoms and molecules</atitle><date>2008-08-15</date><risdate>2008</risdate><abstract>Comm. Pure Appl. Math. 63 (2010), no. 1, 39--118 We prove the first correction to the leading Thomas-Fermi energy for the
ground state energy of atoms and molecules in a model where the kinetic energy
of the electrons is treated relativistically. The leading Thomas-Fermi energy,
established in [Sorensen], as well as the correction given here are of
semi-classical nature. Our result on atoms and molecules is proved from a
general semi-classical estimate for relativistic operators with potentials with
Coulomb-like singularities. This semi-classical estimate is obtained using the
coherent state calculus introduced in [Solovej-Spitzer]. The paper contains a
unified treatment of the relativistic as well as the non-relativistic case.</abstract><doi>10.48550/arxiv.0808.2163</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Mathematical Physics Mathematics - Spectral Theory Physics - Mathematical Physics |
| title | The relativistic Scott correction for atoms and molecules |
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