Uncertainty relation for Fisher information of D -dimensional single-particle systems with central potentials

An uncertainty Fisher information relation in quantum mechanics is derived for multidimensional single-particle systems with central potentials. It is based on the concept of Fisher information in the two complementary position and momentum spaces, which is a gradient functional of the corresponding...

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Bibliographic Details
Published in:Journal of mathematical physics 2006-10, Vol.47 (10), p.103504-103504-11
Main Authors: Romera, Elvira, Sánchez-Moreno, P., Dehesa, J. S.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematical methods in physics
Mathematics
Physics
Quantum theory
Sciences and techniques of general use
Uncertainty
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Summary:An uncertainty Fisher information relation in quantum mechanics is derived for multidimensional single-particle systems with central potentials. It is based on the concept of Fisher information in the two complementary position and momentum spaces, which is a gradient functional of the corresponding probability distributions. The lower bound of the product of position and momentum Fisher informations is shown to depend on the orbital and magnetic quantum numbers of the physical state and the space dimensionality. Applications to various elementary systems is discussed.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2357998