Visualization and dimensional scaling for some three-body problems in atomic and molecular quantum mechanics
Three-body problems in atomic and molecular quantum mechanics, comprising one electron–two nuclei and two electron–one nucleus, are studied from their Schrödinger–Born–Oppenheimer models. The following are main topics of interest in this paper: (1) review of foundational mathematical properties of t...
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| Veröffentlicht in: | Journal of mathematical physics 2008-06, Vol.49 (6), p.062102-062102-57 |
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| container_end_page | 062102-57 |
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| container_issue | 6 |
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| container_title | Journal of mathematical physics |
| container_volume | 49 |
| creator | Chen, Goong Ding, Zhonghai Perronnet, Alain Zhang, Zhigang |
| description | Three-body problems in atomic and molecular quantum mechanics, comprising one electron–two nuclei and two electron–one nucleus, are studied from their Schrödinger–Born–Oppenheimer models. The following are main topics of interest in this paper: (1) review of foundational mathematical properties of the multiparticle Schrödinger operator, (2) visualization of
H
2
+
(hydrogen molecular ion)-like and He (helium)-like molecular and atomic states, and (3) spectrum of He obtained by the large-dimension scaling limit. The authors begin with topic (1) for the tutorial purpose and devote topics (2) and (3) to new contributions of the analytical, numerical, and visualization nature. Relevant heuristics, graphics, proofs, and calculations are presented. |
| doi_str_mv | 10.1063/1.2937002 |
| format | Article |
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H
2
+
(hydrogen molecular ion)-like and He (helium)-like molecular and atomic states, and (3) spectrum of He obtained by the large-dimension scaling limit. The authors begin with topic (1) for the tutorial purpose and devote topics (2) and (3) to new contributions of the analytical, numerical, and visualization nature. Relevant heuristics, graphics, proofs, and calculations are presented.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.2937002</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>BORN-OPPENHEIMER APPROXIMATION ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; ELECTRONS ; Exact sciences and technology ; HELIUM IONS ; HYDROGEN IONS 2 PLUS ; Mathematical methods in physics ; Mathematics ; Physics ; QUANTUM MECHANICS ; Quantum theory ; SCHROEDINGER EQUATION ; Sciences and techniques of general use ; THREE-BODY PROBLEM</subject><ispartof>Journal of mathematical physics, 2008-06, Vol.49 (6), p.062102-062102-57</ispartof><rights>American Institute of Physics</rights><rights>2008 American Institute of Physics</rights><rights>2008 INIST-CNRS</rights><rights>Copyright American Institute of Physics Jun 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c439t-31311129c3a5166c74d4e2ab59d766c300a0c6b2eba5142b49c891acdcb8a5da3</citedby><cites>FETCH-LOGICAL-c439t-31311129c3a5166c74d4e2ab59d766c300a0c6b2eba5142b49c891acdcb8a5da3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.2937002$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>230,314,776,780,790,881,1553,4498,27901,27902,76126,76132</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20498743$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/21100312$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Chen, Goong</creatorcontrib><creatorcontrib>Ding, Zhonghai</creatorcontrib><creatorcontrib>Perronnet, Alain</creatorcontrib><creatorcontrib>Zhang, Zhigang</creatorcontrib><title>Visualization and dimensional scaling for some three-body problems in atomic and molecular quantum mechanics</title><title>Journal of mathematical physics</title><description>Three-body problems in atomic and molecular quantum mechanics, comprising one electron–two nuclei and two electron–one nucleus, are studied from their Schrödinger–Born–Oppenheimer models. The following are main topics of interest in this paper: (1) review of foundational mathematical properties of the multiparticle Schrödinger operator, (2) visualization of
H
2
+
(hydrogen molecular ion)-like and He (helium)-like molecular and atomic states, and (3) spectrum of He obtained by the large-dimension scaling limit. The authors begin with topic (1) for the tutorial purpose and devote topics (2) and (3) to new contributions of the analytical, numerical, and visualization nature. Relevant heuristics, graphics, proofs, and calculations are presented.</description><subject>BORN-OPPENHEIMER APPROXIMATION</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>ELECTRONS</subject><subject>Exact sciences and technology</subject><subject>HELIUM IONS</subject><subject>HYDROGEN IONS 2 PLUS</subject><subject>Mathematical methods in physics</subject><subject>Mathematics</subject><subject>Physics</subject><subject>QUANTUM MECHANICS</subject><subject>Quantum theory</subject><subject>SCHROEDINGER EQUATION</subject><subject>Sciences and techniques of general use</subject><subject>THREE-BODY PROBLEM</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNqNkU1rVTEQhoMoeK0u_AdBcWHhtJkk5yMboRS_oOCmug1zkhybck5ym-QU6q9vbu9FcWFxFSbzvC8z7xDyGtgJsE6cwglXomeMPyEbYINq-q4dnpJN_eENl8PwnLzI-ZoxgEHKDZl_-Lzi7H9h8TFQDJZav7iQa4Uzzab2wk86xURzXBwtV8m5Zoz2jm5THGe3ZOqrrsTFmwf5Emdn1hkTvVkxlHWhizNXGLzJL8mzCefsXh3eI_L908fL8y_NxbfPX8_PLhojhSqNAAEAXBmBLXSd6aWVjuPYKtvXUjCGzHQjd2PtSz5KZQYFaKwZB2wtiiPydu8bc_E6G1_qBCaG4EzRHIAxAbxSb_ZUXeRmdbno67imunWuTNtBr0Rbofd7yKSYc3KT3ia_YLrTwPQucQ36kHhl3x0McZfblDAYn38LOJNq6KWo3Ic9t5vsIfd_m_51Hl3z1dZXg-P_NngMvo3pD6i3dhL34dqyHQ</recordid><startdate>20080601</startdate><enddate>20080601</enddate><creator>Chen, Goong</creator><creator>Ding, Zhonghai</creator><creator>Perronnet, Alain</creator><creator>Zhang, Zhigang</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20080601</creationdate><title>Visualization and dimensional scaling for some three-body problems in atomic and molecular quantum mechanics</title><author>Chen, Goong ; Ding, Zhonghai ; Perronnet, Alain ; Zhang, Zhigang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c439t-31311129c3a5166c74d4e2ab59d766c300a0c6b2eba5142b49c891acdcb8a5da3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>BORN-OPPENHEIMER APPROXIMATION</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>ELECTRONS</topic><topic>Exact sciences and technology</topic><topic>HELIUM IONS</topic><topic>HYDROGEN IONS 2 PLUS</topic><topic>Mathematical methods in physics</topic><topic>Mathematics</topic><topic>Physics</topic><topic>QUANTUM MECHANICS</topic><topic>Quantum theory</topic><topic>SCHROEDINGER EQUATION</topic><topic>Sciences and techniques of general use</topic><topic>THREE-BODY PROBLEM</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Goong</creatorcontrib><creatorcontrib>Ding, Zhonghai</creatorcontrib><creatorcontrib>Perronnet, Alain</creatorcontrib><creatorcontrib>Zhang, Zhigang</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Goong</au><au>Ding, Zhonghai</au><au>Perronnet, Alain</au><au>Zhang, Zhigang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Visualization and dimensional scaling for some three-body problems in atomic and molecular quantum mechanics</atitle><jtitle>Journal of mathematical physics</jtitle><date>2008-06-01</date><risdate>2008</risdate><volume>49</volume><issue>6</issue><spage>062102</spage><epage>062102-57</epage><pages>062102-062102-57</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>Three-body problems in atomic and molecular quantum mechanics, comprising one electron–two nuclei and two electron–one nucleus, are studied from their Schrödinger–Born–Oppenheimer models. The following are main topics of interest in this paper: (1) review of foundational mathematical properties of the multiparticle Schrödinger operator, (2) visualization of
H
2
+
(hydrogen molecular ion)-like and He (helium)-like molecular and atomic states, and (3) spectrum of He obtained by the large-dimension scaling limit. The authors begin with topic (1) for the tutorial purpose and devote topics (2) and (3) to new contributions of the analytical, numerical, and visualization nature. Relevant heuristics, graphics, proofs, and calculations are presented.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.2937002</doi><tpages>57</tpages></addata></record> |
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| source | AIP Journals Complete; AIP Digital Archive |
| subjects | BORN-OPPENHEIMER APPROXIMATION CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ELECTRONS Exact sciences and technology HELIUM IONS HYDROGEN IONS 2 PLUS Mathematical methods in physics Mathematics Physics QUANTUM MECHANICS Quantum theory SCHROEDINGER EQUATION Sciences and techniques of general use THREE-BODY PROBLEM |
| title | Visualization and dimensional scaling for some three-body problems in atomic and molecular quantum mechanics |
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