`BookProof.ChapterAngularMomentum.angularMomentum_eigen` {u : ℂ → ℂ} {μ : ℝ} {z : ℂ} (hdiff : DifferentiableAt ℝ u z) (hequiv : ∀ t : ℝ, u (Complex.exp ((t : ℂ) * Complex.I) * z) =

Proved

BookProof.ChapterAngularMomentum.angularMomentum_eigen

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAngularMomentum.

BookProof.ChapterAngularMomentum.angularMomentum_eigen {u : ℂ → ℂ} {μ : ℝ} {z : ℂ} (hdiff : DifferentiableAt ℝ u z) (hequiv : ∀ t : ℝ, u (Complex.exp ((t : ℂ) * Complex.I) * z) = Complex.exp ((μ : ℂ) * (t : ℂ) * Complex.I) * u z) : -Complex.I * (z.re * fderiv ℝ u z Complex.I - z.im * fderiv ℝ u z 1) = (μ : ℂ) * u z

Formalization note: Lean 4 identifier BookProof.ChapterAngularMomentum.angularMomentum_eigen.

Preamble

-- Generated from ChapterAngularMomentum.lean — theorem BookProof.ChapterAngularMomentum.angularMomentum_eigen
import Mathlib
import Definitions.Def_ChapterAngularMomentum
open BookProof.ChapterAngularMomentum



open Complex

Formal statement

theorem BookProof.ChapterAngularMomentum.angularMomentum_eigen {u : ℂ → ℂ} {μ : ℝ} {z : ℂ}
    (hdiff : DifferentiableAt ℝ u z)
    (hequiv : ∀ t : ℝ, u (Complex.exp ((t : ℂ) * Complex.I) * z)
      = Complex.exp ((μ : ℂ) * (t : ℂ) * Complex.I) * u z) :
    -Complex.I * (z.re * fderiv ℝ u z Complex.I - z.im * fderiv ℝ u z 1) = (μ : ℂ) * u z := by sorry

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