Publication: Propagating-wave approximation in two-dimensional potential scattering
dc.contributor.coauthor | Loran, Farhang | |
dc.contributor.department | Department of Mathematics | |
dc.contributor.kuauthor | Mostafazadeh, Ali | |
dc.contributor.schoolcollegeinstitute | College of Sciences | |
dc.date.accessioned | 2024-11-09T23:39:28Z | |
dc.date.issued | 2022 | |
dc.description.abstract | We 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.indexedby | WOS | |
dc.description.indexedby | Scopus | |
dc.description.issue | 3 | |
dc.description.openaccess | YES | |
dc.description.publisherscope | International | |
dc.description.sponsoredbyTubitakEu | N/A | |
dc.description.sponsorship | Scientific and Technological Research Council of Turkey (TUEB ?ITAK) | |
dc.description.sponsorship | Turkish 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.volume | 106 | |
dc.identifier.doi | 10.1103/PhysRevA.106.032207 | |
dc.identifier.eissn | 2469-9934 | |
dc.identifier.issn | 2469-9926 | |
dc.identifier.quartile | Q2 | |
dc.identifier.scopus | 2-s2.0-85138156538 | |
dc.identifier.uri | https://doi.org/10.1103/PhysRevA.106.032207 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14288/13124 | |
dc.identifier.wos | 863194700001 | |
dc.keywords | Transfer-matrix method | |
dc.keywords | 3-dimensional systems | |
dc.keywords | Anisotropic media | |
dc.keywords | Conductivity | |
dc.keywords | Localization | |
dc.keywords | Formulation | |
dc.keywords | Refraction | |
dc.language.iso | eng | |
dc.publisher | American Physical Society (APS) | |
dc.relation.ispartof | Physical Review A | |
dc.subject | Optics | |
dc.subject | Physics | |
dc.subject | Atomic, molecular and chemical physics | |
dc.title | Propagating-wave approximation in two-dimensional potential scattering | |
dc.type | Journal Article | |
dspace.entity.type | Publication | |
local.contributor.kuauthor | Mostafazadeh, Ali | |
local.publication.orgunit1 | College of Sciences | |
local.publication.orgunit2 | Department of Mathematics | |
relation.isOrgUnitOfPublication | 2159b841-6c2d-4f54-b1d4-b6ba86edfdbe | |
relation.isOrgUnitOfPublication.latestForDiscovery | 2159b841-6c2d-4f54-b1d4-b6ba86edfdbe | |
relation.isParentOrgUnitOfPublication | af0395b0-7219-4165-a909-7016fa30932d | |
relation.isParentOrgUnitOfPublication.latestForDiscovery | af0395b0-7219-4165-a909-7016fa30932d |
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