Author Correction: Incompatible Coulomb hamiltonian extensions

www.nature.com/scientificreports OPEN Author Correction: Incompatible Coulomb hamiltonian extensions G. Abramovici Correction to: Scientific Reports https://doi.org/10.1038/s41598-020-62144-2, published online 29 April 2020 This Article contains errors in Figures 1 and 4. In Figure 1, some of the curves are incorrect due to a change in the behaviour of the function « HarmonicNumber » in Mathematica since the figure was created in 2015. In Figure 4, the curves have not been normalised as stated in the legend, leading to scaling change in the y-axis. The correct Figures 1 and 4 appear below as Figures 1 and 2 respectively. Scientific Reports | (2020) 10:11170 | https://doi.org/10.1038/s41598-020-68526-w 1 Vol.:(0123456789) www.nature.com/scientificreports/ Figure 1.  Here are the curves η → �ϕ−  |ϕ−  �, for n =  − 1/2 (dashed line), n =  − 3/4 (dotted line), n =  − 1 2n 2η (plain line), n =  − 5/4 (dot-dashed line), n =  − 3/2 (dashed line), n =  − 7/4 (dotted line) and n =  − 2 (plain line).  The zeros of each curve read η = 2√−e where e ∈ Sω, with ω =  − gb(n), as explained further on. The curves seem to form pairs corresponding to (n, n + 1), in particular, one could believe that each pair intersects on the η-axis (abscissa), but this is wrong, except for (n, n + 1) = (− 2, − 1) which correspond to the same Rydberg set S∞. All the other intersections are only close to zero, so that, indeed, S−gb (n) �= S−gb (n+1). η = n is missing, because �ϕ−  |ϕ−  � � = 0. 2n 2n   Figure 2.  Here is a zoom of Fig. 1 in the interval − 12 , 0 . Scientific Reports | Vol:.(1234567890) (2020) 10:11170 | https://doi.org/10.1038/s41598-020-68526-w 2 www.nature.com/scientificreports/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. © The Author(s) 2020 Scientific Reports | (2020) 10:11170 | https://doi.org/10.1038/s41598-020-68526-w 3 Vol.:(0123456789)  (...truncated)