Publication:
Application of pseudo-Hermitian quantum mechanics to a PT-symmetric Hamiltonian with a continuum of scattering states

dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorMostafazadeh, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T12:01:14Z
dc.date.issued2005
dc.description.abstractWe extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum. For this potential that has recently been used, in the context of optical potentials, for modeling the propagation of electromagnetic waves traveling in a waveguide half and half filled with gain and absorbing media, we give a perturbative construction of the physical Hilbert space, observables, localized states, and the equivalent Hermitian Hamiltonian. Ignoring terms of order three or higher in the non-Hermiticity parameter zeta, we show that the equivalent Hermitian Hamiltonian has the form p(2)/2m+(zeta(2)/2)Sigma(infinity)(n=0){alpha(n)(x),p(2n)} with alpha(n)(x) vanishing outside an interval that is three times larger than the support of v(x), i.e., in 2/3 of the physical interaction region the potential v(x) vanishes identically. We provide a physical interpretation for this unusual behavior and comment on the classical limit of the system.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue10
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipN/A
dc.description.versionPublisher version
dc.description.volume46
dc.identifier.doi10.1063/1.2063168
dc.identifier.eissn1089-7658
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR00565
dc.identifier.issn0022-2488
dc.identifier.quartileQ3
dc.identifier.scopus2-s2.0-27844491901
dc.identifier.urihttps://hdl.handle.net/20.500.14288/962
dc.identifier.wos232938300008
dc.keywordsNondiagonalizable Hamiltonians
dc.keywordsSquare-Well
dc.keywordsPotentials
dc.keywordsOperators
dc.keywordsSpectrum
dc.language.isoeng
dc.publisherAmerican Institute of Physics (AIP) Publishing
dc.relation.ispartofJournal of Mathematical Physics
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/631
dc.subjectPhysics, Mathematical
dc.titleApplication of pseudo-Hermitian quantum mechanics to a PT-symmetric Hamiltonian with a continuum of scattering states
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMostafazadeh, Ali
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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