dorsal/arxiv
View SchemaExistence of Time Operator for a Singular Harmonic Oscillator
| Authors | V. Mikuta-Martinis, M. Martinis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503187 |
| URL | https://arxiv.org/abs/quant-ph/0503187 |
Abstract
The time operator for a quantum singular oscillator of the Calogero-Sutherland type is constructed in terms of the generators of the SU(1,1) group. In the space spanned by the eigenstates of the Hamiltonian, the time operator is not self-adjoint. We show, that the time-energy uncertainty relation can be given the meaning within the Barut-Girardello coherent states defined for the singular oscillator.We have also shown the relationship with the time-of-arrival operator of Aharonov and Bohm.
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"date_created": "2026-03-02T18:02:15.884000Z",
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"abstract": "The time operator for a quantum singular oscillator of the\nCalogero-Sutherland type is constructed in terms of the generators of the\nSU(1,1) group. In the space spanned by the eigenstates of the Hamiltonian, the\ntime operator is not self-adjoint. We show, that the time-energy uncertainty\nrelation can be given the meaning within the Barut-Girardello coherent states\ndefined for the singular oscillator.We have also shown the relationship with\nthe time-of-arrival operator of Aharonov and Bohm.",
"arxiv_id": "quant-ph/0503187",
"authors": [
"V. Mikuta-Martinis",
"M. Martinis"
],
"categories": [
"quant-ph"
],
"title": "Existence of Time Operator for a Singular Harmonic Oscillator",
"url": "https://arxiv.org/abs/quant-ph/0503187"
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