Publication:
Propagating-wave approximation in two-dimensional potential scattering

dc.contributor.coauthorLoran, Farhang
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorMostafazadeh, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T23:39:28Z
dc.date.issued2022
dc.description.abstractWe introduce a nonperturbative approximation scheme for performing scattering calculations in two dimensions that involves neglecting the contribution of the evanescent waves to the scattering amplitude. This corresponds to replacing the interaction potential v with an associated energy-dependent nonlocal potential V-k that does not couple to the evanescent waves. The scattering solutions psi(r) of the Schrodinger equation, (- del(2) + V-k)psi(r) = k(2)psi(r), have the remarkable property that their Fourier transform (psi)over tilde(p) vanishes unless p corresponds to the momentum of a classical particle whose magnitude equals k. We construct a transfer matrix for this class of nonlocal potentials and explore its representation in terms of the evolution operator for an effective nonunitary quantum system. We show that the above approximation reduces to the first Born approximation for weak potentials and, similar to the semiclassical approximation, becomes valid at high energies. Furthermore, we identify an infinite class of complex potentials for which this approximation scheme is exact. We also discuss the appealing practical and mathematical aspects of this scheme.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue3
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TUEB ?ITAK)
dc.description.sponsorshipTurkish Academy of Sciences (Tuerkiye Bilimler Akademisi) [120F061] This work has been supported by the Scientific and Technological Research Council of Turkey (TUEB ?ITAK) in theframework of Project No. 120F061, and by the Turkish Academy of Sciences (Tuerkiye Bilimler Akademisi).
dc.description.volume106
dc.identifier.doi10.1103/PhysRevA.106.032207
dc.identifier.eissn2469-9934
dc.identifier.issn2469-9926
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-85138156538
dc.identifier.urihttps://doi.org/10.1103/PhysRevA.106.032207
dc.identifier.urihttps://hdl.handle.net/20.500.14288/13124
dc.identifier.wos863194700001
dc.keywordsTransfer-matrix method
dc.keywords3-dimensional systems
dc.keywordsAnisotropic media
dc.keywordsConductivity
dc.keywordsLocalization
dc.keywordsFormulation
dc.keywordsRefraction
dc.language.isoeng
dc.publisherAmerican Physical Society (APS)
dc.relation.ispartofPhysical Review A
dc.subjectOptics
dc.subjectPhysics
dc.subjectAtomic, molecular and chemical physics
dc.titlePropagating-wave approximation in two-dimensional potential scattering
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMostafazadeh, Ali
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
relation.isOrgUnitOfPublication2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isParentOrgUnitOfPublicationaf0395b0-7219-4165-a909-7016fa30932d
relation.isParentOrgUnitOfPublication.latestForDiscoveryaf0395b0-7219-4165-a909-7016fa30932d

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
IR04196.pdf
Size:
627.36 KB
Format:
Adobe Portable Document Format