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ohno merged 1 commit into from
Aug 12, 2026
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Add hydrogen benchmark comparison #45

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22 changes: 22 additions & 0 deletions docs/src/index.md
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Expand Up @@ -86,6 +86,28 @@ axislegend(axis, position=:rt, framevisible=false)
fig
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## Hydrogen atom benchmark

The following table compares the two lowest ``s``-wave energies of the
hydrogen atom in atomic units. Here ``n=0`` denotes the ground state and
``n=1`` the first excited state. The numerical values use the example settings
from the corresponding method pages: 20 Gaussian functions for RR, the
nine-function complement basis (``M_n=9``) for FC, ``\Delta r=0.1`` and
``r_\mathrm{max}=50`` for FDM, the default 1024-point grid
(``\mathtt{quantics}=10``) for QTT+DMRG, and the documented training or
sampling settings for VNN and VMC. A dash indicates that the state is not
currently available.

| Method | ``n=0`` | ``n=1`` |
|:---|---:|---:|
| [RR](@ref Rayleigh-Ritz-Method) | -0.499981735104 | -0.124997703473 |
| [FC](@ref Free-Complement-Method) | -0.499999999978 | -0.123665583532 |
| [FDM](@ref Finite-Difference-Method) | -0.498756211209 | -0.124921972504 |
| [QTT+DMRG](@ref Quantics-Tensor-Train) | -0.499702911360 | -0.124981415403 |
| [VNN](@ref Variational-Neural-Network) | -0.468779111883 | — |
| [VMC](@ref Variational-Monte-Carlo) | -0.480218518855 | — |
| Exact | -0.500000000000 | -0.125000000000 |

## API reference

```@index
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