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The Lévy wave packet and fractional uncertainty relations
Abstract
This work revisits the debate on fractional uncertainty relations that arose a decade ago and tries to settle it. After a careful study of the position-momentum uncertainty product of the Lévy wave packet, a novel lower bound is proposed for uncertainty relations in fractional quantum mechanics. This bound is nearly linear in the Lévy index and is satisfied by exact, calculable solutions available in the literature.
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BibTeX
@misc{li2026lévy,
title = {{The Lévy wave packet and fractional uncertainty relations}},
author = {Zi-Xuan Li and Xiao-Dong Li and Towe Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29397},
eprint = {2610.29397},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29397},
}
RIS
TY - UNPB
TI - The Lévy wave packet and fractional uncertainty relations
AU - Zi-Xuan Li
AU - Xiao-Dong Li
AU - Towe Wang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29397
UR - https://arxiv.org/abs/2610.29397
AB - This work revisits the debate on fractional uncertainty relations that arose a decade ago and tries to settle it. After a careful study of the position-momentum uncertainty product of the Lévy wave packet, a novel lower bound is proposed for uncertainty relations in fractional quantum mechanics. This bound is nearly linear in the Lévy index and is satisfied by exact, calculable solutions available in the literature.
ER -