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feat(QuantumMechanics): Resolvent identities#1188

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feat(QuantumMechanics): Resolvent identities#1188
gloges wants to merge 7 commits into
leanprover-community:masterfrom
gloges:resolvent

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@gloges

@gloges gloges commented Jun 15, 2026

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Adds the following two resolvent identities:

  • R T₁ z - R T₂ z = R T₁ z * (T₂ - T₁) * R T₂ z
  • R T z₁ - R T z₂ = (z₁ - z₂) • (R T z₁ * R T z₂)

To do this requires first fleshing out more properties of compRestricted:

  • Distributivity: (g₁ + g₂) ∘ᵣ f = g₁ ∘ᵣ f + g₂ ∘ᵣ f and g ∘ᵣ (f₁ + f₂) ≥ g ∘ᵣ f₁ + g ∘ᵣ f₂,
  • Scalar multiplication: (c • g) ∘ᵣ f = c • (g ∘ᵣ f) = g ∘ᵣ (c • f) (the latter requires c ≠ 0),
  • Inverses: f⁻¹ ∘ᵣ f = 1 and f ∘ᵣ f⁻¹ = 1 (with appropriate domain restrictions of "1").

@gloges

gloges commented Jun 15, 2026

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t-quantum-mechanics

@github-actions github-actions Bot added the t-quantum-mechanics Quantum mechanics label Jun 15, 2026
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