Comment on “Entropy and complexity analysis of hydrogenic Rydberg atoms” [J. Math. Phys. 54, 052109 (2013)

Abstract

In a recent paper [S. López-Rosa et al., J. Math. Phys. 54, 052109 (2013)], the authors made detailed investigations on the information-theoretic quantities for hydrogenic atoms in Rydberg states. Asymptotic forms of different types of complexity measures (Crámer-Rao, Fisher-Shannon, and LMC types) in both position and momentum spaces were obtained for hydrogenic states (n,l,m) with fixed l and increasingly large n. However, the expressions for the Crámer-Rao complexity are incorrect due to the wrong definition of variance. The correct form of this complexity in position space is presented exactly in this work. In momentum space, two different definitions of variance are provided and corresponding Crámer-Rao complexities are discussed separately. In either case, the momentum complexity increases much faster than that in position space when increasing principal quantum number n.