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Spectral variational principle for Green's functions

dc.contributor.authorBlinder, S. M.en_US
dc.date.accessioned2006-09-11T17:48:01Z
dc.date.available2006-09-11T17:48:01Z
dc.date.issued1972-12en_US
dc.identifier.citationBlinder, S. M.; (1972). "Spectral variational principle for Green's functions." Theoretica Chimica Acta 24(4): 382-388. <http://hdl.handle.net/2027.42/46453>en_US
dc.identifier.issn0040-5744en_US
dc.identifier.issn1432-2234en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/46453
dc.description.abstractFor a suitable approximation ( q, q′, τ ) to the Dirac-Feynman Green's function of a quantummechanical system, the parameter is defined, where ℒ≡ i ∂/∂τ−ℋ. It is shown that Δ ≧0 and Δ →0 as K→K , the exact Green's function, thus providing a criterion on approximate Green's functions analogous in its role to the variational principle for wavefunctions. A second somewhat weaker criterion is also proposed, based on . Recipes are given for projecting out continuum contributions to Δ or ∑ and for analyzing for the discrete eigen-value spectrum. Um zu Näherungen ( q, q′, τ) für die Dirac-Feynman-Greensche Funktion eines quantenmechanischen Systems zu gelangen, wird der Parameter definiert, wobei ℒ≡ i ∂/∂τ−ℋ für iδ/δτ — ℋ steht. Es wird gezeigt, daß Δ ≧0 und Δ →0 wenn K→K , so daß damit ein Kriterium für Näherungen der Green'schen Funktion analog dem Variationsprinzip für Wellenfunktionen gefunden ist. Als zweites, wenn auch schwächeres Kriterium gründet sich auf . Hinweise für das Herausprojizieren der Beträge des Kontinuums aus Δ bzw. ∑ und für die Analyse des diskreten Spektrums werden gegeben.en_US
dc.format.extent316704 bytes
dc.format.extent3115 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_US
dc.publisherSpringer-Verlagen_US
dc.subject.otherOrganic Chemistryen_US
dc.subject.otherChemistryen_US
dc.subject.otherInorganic Chemistryen_US
dc.subject.otherPhysical Chemistryen_US
dc.subject.otherTheoretical and Computational Chemistryen_US
dc.titleSpectral variational principle for Green's functionsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelMaterials Science and Engineeringen_US
dc.subject.hlbsecondlevelChemistryen_US
dc.subject.hlbsecondlevelChemical Engineeringen_US
dc.subject.hlbtoplevelScienceen_US
dc.subject.hlbtoplevelEngineeringen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumCentre de Mécanique Ondulatoire Appliquée, 23 rue du Maroc, Paris 19e, France; Mathematical Institute, University of Oxford, 24-29 St Giles, OX1 3LB, Oxford, Great Britain; Department of Chemistry, University of Michigan, 48104, Ann Arbor, Michiganen_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/46453/1/214_2004_Article_BF01007554.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1007/BF01007554en_US
dc.identifier.sourceTheoretica Chimica Actaen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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