Publication: Application of pseudo-Hermitian quantum mechanics to a PT-symmetric Hamiltonian with a continuum of scattering states
dc.contributor.department | Department of Mathematics | |
dc.contributor.kuauthor | Mostafazadeh, Ali | |
dc.contributor.schoolcollegeinstitute | College of Sciences | |
dc.date.accessioned | 2024-11-09T12:01:14Z | |
dc.date.issued | 2005 | |
dc.description.abstract | We 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.fulltext | YES | |
dc.description.indexedby | WOS | |
dc.description.indexedby | Scopus | |
dc.description.issue | 10 | |
dc.description.openaccess | YES | |
dc.description.publisherscope | International | |
dc.description.sponsoredbyTubitakEu | N/A | |
dc.description.sponsorship | N/A | |
dc.description.version | Publisher version | |
dc.description.volume | 46 | |
dc.identifier.doi | 10.1063/1.2063168 | |
dc.identifier.eissn | 1089-7658 | |
dc.identifier.embargo | NO | |
dc.identifier.filenameinventoryno | IR00565 | |
dc.identifier.issn | 0022-2488 | |
dc.identifier.quartile | Q3 | |
dc.identifier.scopus | 2-s2.0-27844491901 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14288/962 | |
dc.identifier.wos | 232938300008 | |
dc.keywords | Nondiagonalizable Hamiltonians | |
dc.keywords | Square-Well | |
dc.keywords | Potentials | |
dc.keywords | Operators | |
dc.keywords | Spectrum | |
dc.language.iso | eng | |
dc.publisher | American Institute of Physics (AIP) Publishing | |
dc.relation.ispartof | Journal of Mathematical Physics | |
dc.relation.uri | http://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/631 | |
dc.subject | Physics, Mathematical | |
dc.title | Application of pseudo-Hermitian quantum mechanics to a PT-symmetric Hamiltonian with a continuum of scattering states | |
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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