dorsal/arxiv
View SchemaChoice of a Metric for the Non-Hermitian Oscillator
| Authors | D. P. Musumbu, H. B. Geyer, W. D. Heiss |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611150 |
| URL | https://arxiv.org/abs/quant-ph/0611150 |
Abstract
The 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
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"abstract": "The harmonic oscillator Hamiltonian, when augmented by a non-Hermitian\n$\\cal{PT}$-symmetric part, can be transformed into a Hermitian Hamiltonian.\nThis is achieved by introducing a metric which, in general, renders other\nobservables such as the usual momentum or position as non-Hermitian operators.\nThe metric depends on one real parameter, the full range of which is\ninvestigated. The explicit functional dependence of the metric and each\nassociated Hamiltonian is given. A specific choice of this parameter determines\na specific combination of position and momentum as being an observable; this\ncan be in particular either standard position or momentum, but not both\nsimultaneously. Singularities of the metric are explored and their removability\nis investigated. The physical significance of these findings is discussed",
"arxiv_id": "quant-ph/0611150",
"authors": [
"D. P. Musumbu",
"H. B. Geyer",
"W. D. Heiss"
],
"categories": [
"quant-ph"
],
"title": "Choice of a Metric for the Non-Hermitian Oscillator",
"url": "https://arxiv.org/abs/quant-ph/0611150"
},
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