dorsal/arxiv
View SchemaFejer average and the short term behaviors of a wave packet in infinite square well
| Authors | Quan-Hui Liu, Wei-Hong Qi, Li-Ping Fu, Bambi Hu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011048 |
| URL | https://arxiv.org/abs/quant-ph/0011048 |
Abstract
The first two period behaviors of a quantum wave packet in an infinite square well potential is studied. First, the short term behavior of expectation value of a quantity on an equally weighted wave packet (EWWP) is in classical limit proved to reproduce the Fej'{e}r average of the Fourier series decomposition of the corresponding classical quantity. Second, in order to best mimic the classical behavior, a nice relation between number $N$ of stationary states in the EWWP with the average quantum number $n$ as $N\thickapprox \sqrt{n}$ is revealed. Third, since the Fej\'{e}r average can only approximate the classical quantity, it carries an uncertainty which in large quantum number case is almost the same as the quantum uncertainty.
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"abstract": "The first two period behaviors of a quantum wave packet in an infinite square\nwell potential is studied. First, the short term behavior of expectation value\nof a quantity on an equally weighted wave packet (EWWP) is in classical limit\nproved to reproduce the Fej\u0027{e}r average of the Fourier series decomposition of\nthe corresponding classical quantity. Second, in order to best mimic the\nclassical behavior, a nice relation between number $N$ of stationary states in\nthe EWWP with the average quantum number $n$ as $N\\thickapprox \\sqrt{n}$ is\nrevealed. Third, since the Fej\\\u0027{e}r average can only approximate the classical\nquantity, it carries an uncertainty which in large quantum number case is\nalmost the same as the quantum uncertainty.",
"arxiv_id": "quant-ph/0011048",
"authors": [
"Quan-Hui Liu",
"Wei-Hong Qi",
"Li-Ping Fu",
"Bambi Hu"
],
"categories": [
"quant-ph"
],
"title": "Fejer average and the short term behaviors of a wave packet in infinite square well",
"url": "https://arxiv.org/abs/quant-ph/0011048"
},
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