dorsal/arxiv
View SchemaInfinite matrices may violate the associative law
| Authors | Ofir E. Alon, Nimrod Moiseyev, Asher Peres |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9412007 |
| URL | https://arxiv.org/abs/quant-ph/9412007 |
| DOI | 10.1088/0305-4470/28/6/027 |
| Journal | J.Phys. A28 (1995) 1765-1770 |
Abstract
The momentum operator for a particle in a box is represented by an infinite order Hermitian matrix $P$. Its square $P^2$ is well defined (and diagonal), but its cube $P^3$ is ill defined, because $P P^2\neq P^2 P$. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.
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"abstract": "The momentum operator for a particle in a box is represented by an infinite\norder Hermitian matrix $P$. Its square $P^2$ is well defined (and diagonal),\nbut its cube $P^3$ is ill defined, because $P P^2\\neq P^2 P$. Truncating these\nmatrices to a finite order restores the associative law, but leads to other\ncurious results.",
"arxiv_id": "quant-ph/9412007",
"authors": [
"Ofir E. Alon",
"Nimrod Moiseyev",
"Asher Peres"
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"doi": "10.1088/0305-4470/28/6/027",
"journal_ref": "J.Phys. A28 (1995) 1765-1770",
"title": "Infinite matrices may violate the associative law",
"url": "https://arxiv.org/abs/quant-ph/9412007"
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