Decouplarch: Born Oppenheimer Approximation
Quantum Foundations arc, page 25 of 193. Back to The Pixelated Physics Universe
Who they are
Decouplarch has one line, and says it often: “Separate timescales. take it offline.”
Decouplarch is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Born–Oppenheimer approximation: fast electrons and slow nuclei can be treated separately.
$$ \begin{gathered} \Psi(\mathbf{r},\mathbf{R}) \approx \psi_{\mathbf{R}}(\mathbf{r})\, \chi(\mathbf{R}) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\Psi$ | molecular wavefunction | — |
| $\mathbf{r}$ | electron coordinates | m |
| $\mathbf{R}$ | nuclear coordinates | m |
| $\psi_{\mathbf{R}}$ | electronic wavefunction at fixed nuclei | — |
| $\chi$ | nuclear wavefunction | — |
Sources
Crossovers
Decouplarch meets Adiabram (Adiabatic Theorem). Decouplarch splits fast electrons from slow nuclei. That split rests on Adiabram's theorem: the nuclei move so slowly that the electrons follow, staying in their instantaneous state.
Decouplarch meets Sponara (Hertha Sponer and the Birge–Sponer Method). Decouplarch lets molecules have vibrational levels at all, with nuclei moving on a potential the electrons provide. Sponara counts those levels: the gaps shrink toward the dissociation limit, and extrapolating them estimates the bond energy.
Wear the lore
Concept keywords: Born Oppenheimer Approximation, Decouplarch, Quantum Foundations, physics lore, Pixelated Physics