We’ve been quietly extending the RealQM (Real-Space Quantum Mechanics) framework beyond single atoms, and the results are now in two new lecture notes (Y-6 and Y-7).
The idea is simple: why solve the Schrödinger equation with abstract wavefunctions in Hilbert space when we can just partition the electron density in real space? No Slater determinants, no Gaussian basis sets, no Hartree–Fock orbitals — just two electrons, two density regions, and a grid.
In Lecture Y-6, we applied this to the hydrogen molecule (H₂). It worked beautifully. The two electrons naturally separate into two lobes, the energy converges smoothly, and the physics is transparent.
Then we asked: can we go one step further? Can we do a triatomic ion?
Lecture Y-7 answers that question with a resounding yes. We ran the same RealQM machinery on H₃⁺ — the simplest polyatomic ion in the universe and a key player in interstellar chemistry. Three protons, two electrons, three geometries: equilateral, isosceles, and linear.
The results are clean and physically intuitive. The linear geometry wins, the electrons find their optimal spots along the nuclear axis, and the energy converges to six decimal places in 500 steps. No exotic math. Just a grid, a relaxation scheme, and a physically motivated local electron–electron potential.
What’s nice about this is the simplicity. You don’t need a supercomputer or a quantum-chemistry package. You can run this on a laptop. The code is on GitHub, the plots are included, and the physics is right there in the density maps.
We think this is a nice demonstration that RealQM is not just a toy model for atoms — it’s a genuine alternative for describing small molecular systems, with a much clearer physical picture than conventional methods.
Check out the lectures. And yes — the code is open source. Go have a look.
Links:
- Lecture Y-6: The RealQM Model of H₂
- Lecture Y-7: The RealQM Model of H₃⁺
- GitHub: RealQM-H3
Enjoy.
Jean Louis Van Belle
Reading Feynman 