Choice of a Metric for the Non-Hermitian Oscillator

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dc.creatorMusumbu, D. P.
dc.creatorGeyer, H. B.
dc.creatorHeiss, W. D.
dc.date2006-11-14
dc.date.accessioned2026-07-07T07:34:12Z
dc.date.available2026-07-07T07:34:12Z
dc.descriptionThe harmonic oscillator Hamiltonian, when augmented by a non-Hermitian $\cal{PT}$-symmetric part, can be transformed into a Hermitian Hamiltonian. This is achieved by introducing a metric which, in general, renders other observables such as the usual momentum or position as non-Hermitian operators. The metric depends on one real parameter, the full range of which is investigated. The explicit functional dependence of the metric and each associated Hamiltonian is given. A specific choice of this parameter determines a specific combination of position and momentum as being an observable; this can be in particular either standard position or momentum, but not both simultaneously. Singularities of the metric are explored and their removability is investigated. The physical significance of these findings is discussed
dc.descriptionto appear in J Phys A
dc.identifierhttps://arxiv.org/abs/quant-ph/0611150
dc.identifierhttp://arxiv.org/abs/quant-ph/0611150
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119728
dc.subjectQuantum Physics
dc.titleChoice of a Metric for the Non-Hermitian Oscillator
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