dorsal/arxiv
View SchemaGauss Sums and Quantum Mechanics
| Authors | Vernon Armitage, Alice Rogers |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0003107 |
| URL | https://arxiv.org/abs/quant-ph/0003107 |
| DOI | 10.1088/0305-4470/33/34/305 |
Abstract
By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved. The toroidal nature of the classical phase space leads to discrete position and momentum, and hence discrete time. The corresponding `path integrals' are finite sums whose normalisations are derived and which are shown to intertwine cyclicity and discreteness to give a finite version of Kelvin's method of images.
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"abstract": "By adapting Feynman\u0027s sum over paths method to a quantum mechanical system\nwhose phase space is a torus, a new proof of the Landsberg-Schaar identity for\nquadratic Gauss sums is given. In contrast to existing non-elementary proofs,\nwhich use infinite sums and a limiting process or contour integration, only\nfinite sums are involved. The toroidal nature of the classical phase space\nleads to discrete position and momentum, and hence discrete time. The\ncorresponding `path integrals\u0027 are finite sums whose normalisations are derived\nand which are shown to intertwine cyclicity and discreteness to give a finite\nversion of Kelvin\u0027s method of images.",
"arxiv_id": "quant-ph/0003107",
"authors": [
"Vernon Armitage",
"Alice Rogers"
],
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"quant-ph",
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"doi": "10.1088/0305-4470/33/34/305",
"title": "Gauss Sums and Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0003107"
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