| import Mathlib | |
| import OAI.Analysis.CoulombIonization.Localization.FermionL2 | |
| import OAI.Analysis.CoulombIonization.Localization.PacketFourier | |
| namespace OAI | |
| noncomputable section | |
| open MeasureTheory Filter | |
| open scoped Topology BigOperators ContDiff | |
| open MeasureTheory Filter Complex TopologicalSpace | |
| open scoped Topology InnerProductSpace ENNReal | |
| open MeasureTheory Filter Complex | |
| open scoped Topology BigOperators ComplexConjugate FourierTransform SchwartzMap ENNReal | |
| open MeasureTheory Filter | |
| open scoped Topology ContDiff SchwartzMap FourierTransform ENNReal | |
| open MeasureTheory Filter | |
| open scoped ContDiff InnerProductSpace Topology | |
| open MeasureTheory Filter | |
| open scoped ENNReal | |
| namespace CoulombPackets | |
| open CoulombPauli | |
| variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] | |
| [FiniteDimensional ℝ V] [MeasurableSpace V] [BorelSpace V] | |
| def HasFermionGradient {N : ℕ} {ι : Type*} [Fintype ι] | |
| (b : OrthonormalBasis ι ℝ V) (ψ : fermionL2 (V := V) (N+1)) | |
| (u : Fin (N+1) → ι → fermionL2 (V := V) (N+1)) : Prop := | |
| ∀ i a, HasWeakSpinPartialDerivative (splitFermion i ψ) (splitFermion i (u i a)) (b a) | |
| end CoulombPackets | |
| end | |
| end OAI | |