`BookProof.SmCar.fermiEnergy_quadForm` (m : Fin n → ℝ) (ψ : FermiFock n) : (inner ℂ ψ (fermiEnergy m ψ) : ℂ) = ∑ S : Finset (Fin n), ((∑ i ∈ S, m i : ℝ) : ℂ) * ((‖ψ S‖ ^...

Proved

BookProof.SmCar.fermiEnergy_quadForm

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.fermiEnergy_quadForm (m : Fin n → ℝ) (ψ : FermiFock n) : (inner ℂ ψ (fermiEnergy m ψ) : ℂ) = ∑ S : Finset (Fin n), ((∑ i ∈ S, m i : ℝ) : ℂ) * ((‖ψ S‖ ^ 2 : ℝ) : ℂ)

Formalization note: Lean 4 identifier BookProof.SmCar.fermiEnergy_quadForm.

Preamble

-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.fermiEnergy_quadForm
import Mathlib
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.SmCar



open Finset

variable {n : ℕ}

Formal statement

theorem BookProof.SmCar.fermiEnergy_quadForm (m : Fin n → ℝ) (ψ : FermiFock n) :
    (inner ℂ ψ (fermiEnergy m ψ) : ℂ)
      = ∑ S : Finset (Fin n), ((∑ i ∈ S, m i : ℝ) : ℂ) * ((‖ψ S‖ ^ 2 : ℝ) : ℂ) := by sorry

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