`BookProof.ChapterCoherentOverlap.coherentOverlap_eq` (q k : EuclideanSpace ℝ (Fin n)) : coherentOverlap q k = Real.exp (-(∑ i, q i * q i) / 2 - (∑ i, k i * k i) / 2 + ∑ i, q i * k

Proved

BookProof.ChapterCoherentOverlap.coherentOverlap_eq

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlap.

BookProof.ChapterCoherentOverlap.coherentOverlap_eq (q k : EuclideanSpace ℝ (Fin n)) : coherentOverlap q k = Real.exp (-(∑ i, q i * q i) / 2 - (∑ i, k i * k i) / 2 + ∑ i, q i * k i)

Formalization note: Lean 4 identifier BookProof.ChapterCoherentOverlap.coherentOverlap_eq.

Preamble

-- Generated from ChapterCoherentOverlap.lean — theorem BookProof.ChapterCoherentOverlap.coherentOverlap_eq
import Mathlib
import Definitions.Def_ChapterCoherentOverlap
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteProductCore
open BookProof.ChapterCoherentOverlap


open scoped BigOperators

noncomputable section


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlap.coherentOverlap_eq (q k : EuclideanSpace ℝ (Fin n)) :
    coherentOverlap q k =
      Real.exp (-(∑ i, q i * q i) / 2 - (∑ i, k i * k i) / 2 + ∑ i, q i * k i) := by sorry

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