dorsal/arxiv
View SchemaThe Classical Limit of Quantum Mechanics and the Fejer Sum of the Fourier Series Expansion of a Classical Quantity
| Authors | Q. H. Liu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0008005 |
| URL | https://arxiv.org/abs/quant-ph/0008005 |
| DOI | 10.1088/0305-4470/32/4/003 |
| Journal | Journal of Physics A, 32(1999)L57-L62 |
Abstract
In quantum mechanics, the expectation value of a quantity on a quantum state, provided that the state itself gives in the classical limit a motion of a particle in a definite path, in classical limit goes over to Fourier series form of the classical quantity. In contrast to this widely accepted point of view, a rigorous calculation shows that the expectation value on such a state in classical limit exactly gives the Fej\'{e}r's arithmetic mean of the partial sums of the Fourier series.
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"abstract": "In quantum mechanics, the expectation value of a quantity on a quantum state,\nprovided that the state itself gives in the classical limit a motion of a\nparticle in a definite path, in classical limit goes over to Fourier series\nform of the classical quantity. In contrast to this widely accepted point of\nview, a rigorous calculation shows that the expectation value on such a state\nin classical limit exactly gives the Fej\\\u0027{e}r\u0027s arithmetic mean of the partial\nsums of the Fourier series.",
"arxiv_id": "quant-ph/0008005",
"authors": [
"Q. H. Liu"
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"doi": "10.1088/0305-4470/32/4/003",
"journal_ref": "Journal of Physics A, 32(1999)L57-L62",
"title": "The Classical Limit of Quantum Mechanics and the Fejer Sum of the Fourier Series Expansion of a Classical Quantity",
"url": "https://arxiv.org/abs/quant-ph/0008005"
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