dorsal/arxiv
View SchemaA generalized Weyl relation approach to the time operator and its connection to the survival probability
| Authors | Manabu Miyamoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0006085 |
| URL | https://arxiv.org/abs/quant-ph/0006085 |
| DOI | 10.1063/1.1346598 |
Abstract
The time operator, an operator which satisfies the canonical commutation relation with the Hamiltonian, is investigated, on the basis of a certain algebraic relation for a pair of operators T and H, where T is symmetric and H self-adjoint. This relation is equivalent to the Weyl relation, in the case of self-adjoint T, and is satisfied by the Aharonov-Bohm time operator T_0 and the free Hamiltonian H_0 for the one-dimensional free-particle system. In order to see the qualitative properties of T_0, the operators T and H satisfying this algebraic relation are examined. In particular, it is shown that the standard deviation of T is directly connected to the survival probability, and H is absolutely continuous. Hence, it is concluded that the existence of the operator T implies the existence of scattering states. It is also shown that the minimum uncertainty states do not exist. Other examples of these operators T and H, than the one-dimensional free-particle system, are demonstrated.
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"abstract": "The time operator, an operator which satisfies the canonical commutation\nrelation with the Hamiltonian, is investigated, on the basis of a certain\nalgebraic relation for a pair of operators T and H, where T is symmetric and H\nself-adjoint. This relation is equivalent to the Weyl relation, in the case of\nself-adjoint T, and is satisfied by the Aharonov-Bohm time operator T_0 and the\nfree Hamiltonian H_0 for the one-dimensional free-particle system. In order to\nsee the qualitative properties of T_0, the operators T and H satisfying this\nalgebraic relation are examined. In particular, it is shown that the standard\ndeviation of T is directly connected to the survival probability, and H is\nabsolutely continuous. Hence, it is concluded that the existence of the\noperator T implies the existence of scattering states. It is also shown that\nthe minimum uncertainty states do not exist. Other examples of these operators\nT and H, than the one-dimensional free-particle system, are demonstrated.",
"arxiv_id": "quant-ph/0006085",
"authors": [
"Manabu Miyamoto"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1346598",
"title": "A generalized Weyl relation approach to the time operator and its connection to the survival probability",
"url": "https://arxiv.org/abs/quant-ph/0006085"
},
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