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

Abstract

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.