an:06804345
Zbl 1373.81115
L??pez-Rosa, S.; Toranzo, I. V.; S??nchez-Moreno, P.; Dehesa, J. S.
Response to ``Comment on ``Entropy and complexity analysis of hydrogenic Rydberg atoms'' [J. Math. Phys. 58, 104101 (2017)]
EN
J. Math. Phys. 58, No. 10, 104102, 2 p. (2017).
00371675
2017
j
81P45 94A17 33C45
From the text: In their comment [J. Math. Phys. 58, No. 10, 104101, 4 p. (2017; Zbl 1373.81110)] on our paper [\textit{S. L??pez-Rosa} et al., J. Math. Phys. 54, No. 5, 052109, 18 p. (2013; Zbl 1282.81054)], \textit{L. G. Jiao} and \textit{L. R. Zan} argued that the expressions used for the Cr??mer-Rao complexity in both position and momentum spaces are incorrect due to the wrong definition of variance. Specifically they point out that: (1) the correct form of this complexity in position space is presented exactly in their work; (2) in momentum space, two different definitions of the variance are provided and corresponding Cr??mer-Rao complexities are discussed separately.
There are two underlying issues in the Jiao-Zan comment to our paper1 which are certainly controverted, but not yet fully solved. One is the extension to arbitrary dimensions of the notion of variance of a one-dimensional probability distribution \(\rho(x)\), corresponding to some random variable \(X\) (e.g., position, momentum, \dots) (see, e.g. \textit{M. J. W. Hall}[Phys. Rev A 59, No. 4. 2602--2615 (1999: \url{doi:10.1103/PhysRevA.59.2602})] and \textit{A. Dembo}et al. [IEEE Trans. Inf. Theory 37, No. 6, 1501--1518 (1991; Zbl 0741.94001)]), that is, to a probability distribution \(\rho(\vec{r})\) of a D-dimensional observable \(\vec{r}\). Another issue is the definition of the Cr??mer-Rao complexity so that it approaches as close as possible the intuitive notion of complexity [\textit{L. Rudnicki} et al., Phys. Lett. A 380, No. 3, 377--380 (2016; Zbl 1349.81065)].
Zbl 0741.94001; Zbl 1349.81065; Zbl 1373.81110; Zbl 1282.81054