Semiclassical analysis of a complex quartic Hamiltonian

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dc.creatorBender, Carl M.
dc.creatorBrody, Dorje C.
dc.creatorJones, Hugh F.
dc.date2005-09-05
dc.date.accessioned2026-07-07T11:44:34Z
dc.date.available2026-07-07T11:44:34Z
dc.descriptionIt is necessary to calculate the C operator for the non-Hermitian PT-symmetric Hamiltonian H=\half p^2+\halfμ^2x^2-λx^4 in order to demonstrate that H defines a consistent unitary theory of quantum mechanics. However, the C operator cannot be obtained by using perturbative methods. Including a small imaginary cubic term gives the Hamiltonian H=\half p^2+\half μ^2x^2+igx^3-λx^4, whose C operator can be obtained perturbatively. In the semiclassical limit all terms in the perturbation series can be calculated in closed form and the perturbation series can be summed exactly. The result is a closed-form expression for C having a nontrivial dependence on the dynamical variables x and p and on the parameter λ.
dc.description4 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0509034
dc.identifierhttp://arxiv.org/abs/quant-ph/0509034
dc.identifierPhys.Rev.D73:025002,2006
dc.identifierdoi:10.1103/PhysRevD.73.025002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201649
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.titleSemiclassical analysis of a complex quartic Hamiltonian
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