dorsal/arxiv
View SchemaCharacteristic decay of the autocorrelation functions prescribed by the Aharonov-Bohm time operator
| Authors | Manabu Miyamoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0105033 |
| URL | https://arxiv.org/abs/quant-ph/0105033 |
Abstract
The wave functions, the autocorrelation functions of which decay faster than $t^{-2}$, for both the one-dimensional free particle system and the repulsive-potential system are examined. It is then shown that such wave functions constitute a dense subset of $L^2 ({\bf R}^1)$, under several conditions that are particularly satisfied by the square barrier potential system. It implies that the faster than $t^{-2}$-decay character of the autocorrelation function persists against the perturbation of potential. It is also seen that the denseness of the above subset is guaranteed by that of the domain of the Aharonov-Bohm time operator.
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"abstract": "The wave functions, the autocorrelation functions of which decay faster than\n$t^{-2}$, for both the one-dimensional free particle system and the\nrepulsive-potential system are examined. It is then shown that such wave\nfunctions constitute a dense subset of $L^2 ({\\bf R}^1)$, under several\nconditions that are particularly satisfied by the square barrier potential\nsystem. It implies that the faster than $t^{-2}$-decay character of the\nautocorrelation function persists against the perturbation of potential. It is\nalso seen that the denseness of the above subset is guaranteed by that of the\ndomain of the Aharonov-Bohm time operator.",
"arxiv_id": "quant-ph/0105033",
"authors": [
"Manabu Miyamoto"
],
"categories": [
"quant-ph"
],
"title": "Characteristic decay of the autocorrelation functions prescribed by the Aharonov-Bohm time operator",
"url": "https://arxiv.org/abs/quant-ph/0105033"
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