Updated the description of figure 1

[ohno]

#99

4. Could more details for figure 1 be given, especially with regards to the discrepancy between the numerical and exact forms, and perhaps how far the expansion is pushed. Is it expected that increasing the size of the expansion would resolve the discrepancy?

Please add the expansion range of Gaussian basis, etc. Qualitative and quantitative descriptions of the errors should also be added.

Antique.jl/joss/paper.md

Line 54 in ad463ca

![\label{fig:usage}The radial density of four s-wave states of the hydrogen atom calculated by the Rayleigh-Ritz method, implemented in TwoBody.jl [@TwoBody]. We employed Gaussian basis functions $\phi_n(r) = \exp(-\nu_n r^2)$ whose exponents were determined by the geometric progression defined in the previous study [@Hiyama2018]. The numerical solution (solid blue line) is compared to the analytical solution (dashed black line) using Antique.jl. This figure is drawn using Mekie.jl [@Danisch2021].](./figure.pdf)

[ajarifi]

I think we can add some comments on this in the text. I believe you have numerically checked that the discrepancy can be resolved for some cases. However, some highly excited states may require additional treatment due to their oscillatory behavior.

Deviations from the analytic solutions appear in excited states due to the limited number of basis functions, reflecting the accuracy limits of the numerical method. These deviations diminish with more basis functions, though an optimal number can be chosen for the system of interest.