Publication:
Differential realization of pseudo-Hermiticity: a quantum mechanical analog of Einstein's field equation

dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorMostafazadeh, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T13:46:04Z
dc.date.issued2006
dc.description.abstractFor a given pseudo-Hermitian Hamiltonian of the standard form: H=p(2)/2m+v(x), we reduce the problem of finding the most general (pseudo-)metric operator eta satisfying H(dagger)=eta H eta(-1) to the solution of a differential equation. If the configuration space is R, this is a Klein-Gordon equation with a nonconstant mass term. We obtain a general series solution of this equation that involves a pair of arbitrary functions. These characterize the arbitrariness in the choice of eta. We apply our general results to calculate eta for the PT-symmetric square well, an imaginary scattering potential, and a class of imaginary delta-function potentials. For the first two systems, our method reproduces the known results in a straightforward and extremely efficient manner. For all these systems we obtain the most general eta up to second-order terms in the coupling constants.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue7
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipN/A
dc.description.versionPublisher version
dc.description.volume47
dc.identifier.doi10.1063/1.2212668
dc.identifier.eissn1089-7658
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR00566
dc.identifier.issn0022-2488
dc.identifier.quartileQ3
dc.identifier.scopus2-s2.0-33746807203
dc.identifier.urihttps://hdl.handle.net/20.500.14288/3676
dc.identifier.wos239423800003
dc.keywordsSymmetric square-well
dc.keywordsPt-symmetry
dc.keywordsPoint interactions
dc.keywordsHamiltonians
dc.keywordsSpectrum
dc.keywordsOperator
dc.keywordsOscillator
dc.keywordsScattering
dc.keywordsReality
dc.keywordsModel
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/626
dc.subjectMathematical physics
dc.titleDifferential realization of pseudo-Hermiticity: a quantum mechanical analog of Einstein's field equation
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMostafazadeh, Ali
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isParentOrgUnitOfPublicationaf0395b0-7219-4165-a909-7016fa30932d
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