`BookProof.ChapterBornMeasure.norm_evolve` (H : Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ) (hH : IsSelfAdjoint H) (t : ℝ) (psi : Lp ℂ 2 μ) : ‖evolve H t psi‖ = ‖psi‖

Proved

BookProof.ChapterBornMeasure.norm_evolve

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBornMeasure.

BookProof.ChapterBornMeasure.norm_evolve (H : Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ) (hH : IsSelfAdjoint H) (t : ℝ) (psi : Lp ℂ 2 μ) : ‖evolve H t psi‖ = ‖psi‖

Formalization note: Lean 4 identifier BookProof.ChapterBornMeasure.norm_evolve.

Preamble

-- Generated from ChapterBornMeasure.lean — theorem BookProof.ChapterBornMeasure.norm_evolve
import Mathlib
import Definitions.Def_ChapterBornMeasure
import Definitions.Def_ChapterContinuityUnitary
import Definitions.Def_ChapterContinuityUnitaryInfinite
open BookProof.ChapterContinuityUnitary
open BookProof.ChapterContinuityUnitaryInfinite
open BookProof.ChapterBornMeasure


open MeasureTheory
open scoped ENNReal


variable {α : Type*} [MeasurableSpace α] {μ : Measure α}

Formal statement

theorem BookProof.ChapterBornMeasure.norm_evolve (H : Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ) (hH : IsSelfAdjoint H) (t : ℝ)
    (psi : Lp ℂ 2 μ) : ‖evolve H t psi‖ = ‖psi‖ := by sorry

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