dorsal/arxiv
View SchemaA single particle uncertainty relation
| Authors | Thomas Schürmann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0303005 |
| URL | https://arxiv.org/abs/quant-ph/0303005 |
| Journal | Acta Physica Polonica B 39 (2008) 587-597 |
Abstract
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq. Several upper bounds for the probability P are determined. For arbitrary, but given precision dq, dk, these bounds refer to the variation of q, k and the state vector of the particle. A weak bound is given by the inequality P <= dkdq/h, where h is Planck's quantum of action. It is non-trivial for all measurements with dkdq < h. A sharper bound is obtained by applying the Hilbert-Schmidt-norm. As our main result the least upper bound of P is determined. All bounds are independent of the order with which the measuring of position and momentum is made.
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"abstract": "We consider successive measurements of position and momentum of a single\nparticle. Let P be the conditional probability to measure the momentum k with\nprecision dk, given a previously successful position measurement q with\nprecision dq. Several upper bounds for the probability P are determined. For\narbitrary, but given precision dq, dk, these bounds refer to the variation of\nq, k and the state vector of the particle. A weak bound is given by the\ninequality P \u003c= dkdq/h, where h is Planck\u0027s quantum of action. It is\nnon-trivial for all measurements with dkdq \u003c h. A sharper bound is obtained by\napplying the Hilbert-Schmidt-norm. As our main result the least upper bound of\nP is determined. All bounds are independent of the order with which the\nmeasuring of position and momentum is made.",
"arxiv_id": "quant-ph/0303005",
"authors": [
"Thomas Sch\u00fcrmann"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"physics.atom-ph"
],
"journal_ref": "Acta Physica Polonica B 39 (2008) 587-597",
"title": "A single particle uncertainty relation",
"url": "https://arxiv.org/abs/quant-ph/0303005"
},
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