Update demonstration section

[ohno]

#99

2. The docs are generally very good and very detailled. It is a pleasure to see sources other than wikipedia cited in a code. However, the initial usage section of the documentation which is quite sparse. New users should not be expected to guess the symbols used for wavefunctions and potentials, nor how to access \psi and other greek letters from the terminal or editors of choice. A few extra lines in the Demonstration section would be welcome both to highlight the typography and other main functions.

[ohno]

@ajarifi May I assign this problem to you? Please add examples with descriptions to demonstration section. Here are examples:

using Antique
H = HydrogenAtom(Z=1, Eₕ=1.0, a₀=1.0, mₑ=1.0, ℏ=1.0)

julia> V(H, 0.0)
-Inf

julia> V(H, 1.0)
-1.0

julia> E(H)
-0.5

julia> E(H, n=2)
-0.125

julia> ψ(H, 0.0, 0.0, 0.0)
0.5641895835477564 + 0.0im

julia> abs2(ψ(H, 0.0, 0.0, 0.0))
0.3183098861837908 # ≃ 1/pi

julia> abs2(ψ(H, 0.0, 0.0, 0.0, n=2, l=1))
0.0

The demonstration section is here:

Antique.jl/docs/src/index.md

Lines 97 to 99 in ad463ca

	## Demonstration
	This is an example of a variational calculation for the hydrogen atom based on [Thijssen(2007)](https://doi.org/10.1017/CBO9781139171397). We check the accuracy of the numerical solution by comparison with the analytical solution. Comparing wave functions can be difficult, but Antique.jl makes it easy. You can extend it to excited states ($n>1$) as well as the ground state ($n=1$). Thus, Antique.jl is useful for testing numerical methods. We hope many numerical methods to be developed using Antique.jl.

[ohno]

This is a similar issue: #79.

[ajarifi]

Ok, I will do this part.

[ajarifi]

New users should not be expected to guess the symbols used for wavefunctions and potentials, nor how to access \psi and other greek letters from the terminal or editors of choice. A few extra lines in the Demonstration section would be welcome both to highlight the typography and other main functions.

@ohno, I created a branch demo, I edited the usage and examples by adding the infinite potential well and hydrogen-like atom in the README.md and docs/src/index.md. Probably, the example is too much for README.md.
I also created a table of symbols and Greek letters, which may be useful for the current version.
You are free to remove or edit it as you like.

I think the referee commented on the Usage and examples about the typography and other main functions. The demonstration section is about the numerical testing using Antique.jl. Maybe the demonstration can be added under the usage and examples.

[ajarifi]

If you have some opinions, you can let me know.

[ohno]

@ajarifi Could you please submit a pull request? I would like to see diffs and leave comments.

[ajarifi]

@ohno, Related PR: #106