dorsal/arxiv
View SchemaFree motion time-of-arrival operator and probability distribution
| Authors | I. L. Egusquiza, J. G. Muga |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9905023 |
| URL | https://arxiv.org/abs/quant-ph/9905023 |
| DOI | 10.1103/PhysRevA.61.012104 |
| Journal | Phys.Rev.A61:012104,1999 |
Abstract
We reappraise and clarify the contradictory statements found in the literature concerning the time-of-arrival operator introduced by Aharonov and Bohm in Phys. Rev. {\bf 122}, 1649 (1961). We use Naimark's dilation theorem to reproduce the generalized decomposition of unity (or POVM) from any self-adjoint extension of the operator, emphasizing a natural one, which arises from the analogy with the momentum operator on the half-line. General time operators are set within a unifying perspective. It is shown that they are not in general related to the time of arrival, even though they may have the same form.
{
"annotation_id": "579b5a42-79ae-45a7-a8b6-898628803eb6",
"date_created": "2026-03-02T18:02:47.317000Z",
"date_modified": "2026-03-02T18:02:47.317000Z",
"file_hash": "43b1e592014fbd91d29c2eed47ac1717b50ba5b5f33523dd412f730200d201f9",
"private": false,
"record": {
"abstract": "We reappraise and clarify the contradictory statements found in the\nliterature concerning the time-of-arrival operator introduced by Aharonov and\nBohm in Phys. Rev. {\\bf 122}, 1649 (1961). We use Naimark\u0027s dilation theorem to\nreproduce the generalized decomposition of unity (or POVM) from any\nself-adjoint extension of the operator, emphasizing a natural one, which arises\nfrom the analogy with the momentum operator on the half-line. General time\noperators are set within a unifying perspective. It is shown that they are not\nin general related to the time of arrival, even though they may have the same\nform.",
"arxiv_id": "quant-ph/9905023",
"authors": [
"I. L. Egusquiza",
"J. G. Muga"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.61.012104",
"journal_ref": "Phys.Rev.A61:012104,1999",
"title": "Free motion time-of-arrival operator and probability distribution",
"url": "https://arxiv.org/abs/quant-ph/9905023"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "87d50f38-b49c-469f-9b91-3abc648427a0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}