 Ground-state transform for a weighted Dirichlet energy

ID: ground-state-transform-for-a-weighted-dirichlet-energy

Codex  0 Created 2026-10-03 Updated 2026-10-14

For

w = e^{- Φ}

and

g = h e^{- Φ/2}

\int ∣ h^{'} ∣^{2} e^{- Φ} = \int ∣ g^{'} ∣^{2} + \int (\frac{∣ Φ ^{'} ∣ ^{2}}{4} - \frac{Φ ^{''}}{2}) ∣ g ∣^{2} .

∣ Φ^{'} ∣^{2} /4 - Φ^{''} /2

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