Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics

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dc.creatorBender, Carl M.
dc.creatorJones, Hugh F.
dc.date2004-05-12
dc.date.accessioned2026-07-07T11:32:17Z
dc.date.available2026-07-07T11:32:17Z
dc.descriptionTo determine the Hilbert space and inner product for a quantum theory defined by a non-Hermitian $\mathcal{PT}$-symmetric Hamiltonian $H$, it is necessary to construct a new time-independent observable operator called $C$. It has recently been shown that for the {\it cubic} $\mathcal{PT}$-symmetric Hamiltonian $H=p^2+ x^2+iεx^3$ one can obtain $\mathcal{C}$ as a perturbation expansion in powers of $ε$. This paper considers the more difficult case of noncubic Hamiltonians of the form $H=p^2+x^2(ix)^δ$ ($δ\geq0$). For these Hamiltonians it is shown how to calculate $\mathcal{C}$ by using nonperturbative semiclassical methods.
dc.description11 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/hep-th/0405113
dc.identifierhttp://arxiv.org/abs/hep-th/0405113
dc.identifierPhys.Lett.A328:102-109,2004
dc.identifierdoi:10.1016/j.physleta.2004.05.063
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/197545
dc.subjectHigh Energy Physics - Theory
dc.titleSemiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics
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