Direct numerical solution of the Lippmann-Schwinger equation in coordinate space without partial-wave decomposition

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dc.citation.epage053303-10en_US
dc.citation.issueNumber5en_US
dc.citation.spage053303-1en_US
dc.citation.volumeNumber94en_US
dc.contributor.authorKuruoğlu, Z. C.en_US
dc.date.accessioned2018-04-12T10:43:34Z
dc.date.available2018-04-12T10:43:34Z
dc.date.issued2016en_US
dc.departmentDepartment of Chemistryen_US
dc.description.abstractDirect numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann-Schwinger (LS) equation is considered without invoking the traditional partial-wave decomposition. The singular kernel of the three-dimensional LS equation in coordinate space is regularized by a subtraction technique. The resulting nonsingular integral equation is then solved via the Nystrom method employing a direct-product quadrature rule for three variables. To reduce the computational burden of discretizing three variables, advantage is taken of the fact that, for central potentials, the azimuthal angle can be integrated out, leaving a two-variable reduced integral equation. A regularization method for the kernel of the two-variable integral equation is derived from the treatment of the singularity in the three-dimensional equation. A quadrature rule constructed as the direct product of single-variable quadrature rules for radial distance and polar angle is used to discretize the two-variable integral equation. These two- and three-variable methods are tested on the Hartree potential. The results show that the Nystrom method for the coordinate-space LS equation compares favorably in terms of its ease of implementation and effectiveness with the Nystrom method for the momentum-space version of the LS equation.en_US
dc.description.provenanceMade available in DSpace on 2018-04-12T10:43:34Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2016en
dc.identifier.doi10.1103/PhysRevE.94.053303en_US
dc.identifier.eissn2470-0053
dc.identifier.issn2470-0045
dc.identifier.urihttp://hdl.handle.net/11693/36537
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttps://doi.org/10.1103/PhysRevE.94.053303en_US
dc.source.titlePhysical Review Een_US
dc.subjectSemiconductor quantum wellsen_US
dc.subjectCentral potentialsen_US
dc.subjectComputational burdenen_US
dc.subjectHartree potentialen_US
dc.subjectLippmann-Schwinger equationsen_US
dc.subjectNumerical solutionen_US
dc.subjectRegularization methodsen_US
dc.subjectThree-dimensional equationsen_US
dc.subjectVariable integralen_US
dc.subjectIntegral equationsen_US
dc.titleDirect numerical solution of the Lippmann-Schwinger equation in coordinate space without partial-wave decompositionen_US
dc.typeArticleen_US

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