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New Journal of Physics

Improvement of the Heisenberg and Fisher-information-based uncertainty relations forD-dimensional central potentials

Pablo Sánchez-Moreno, Rosario González‐Férez, J. S. Dehesa

Published Dec 21, 2006• 58 citations
Publisher

Abstract

The Heisenberg and Fisher-information-based uncertainty relations are improved for stationary states of single-particle systems in a D -dimensional central potential. The improvement increases with the squared orbital hyperangular quantum number. The new uncertainty relations saturate for the isotropic harmonic oscillator wavefunction.
DOI
10.1088/1367-2630/8/12/330

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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.
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