`BookProof.HermiteStrichartzQG.oscillator_eigenfunction` (n : ℕ) (x : ℝ) : -(deriv (deriv (hermiteFun n)) x) + x ^ 2 / 4 * hermiteFun n x = oscillatorSymbol n * hermiteFun n x

Proved

BookProof.HermiteStrichartzQG.oscillator_eigenfunction

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterStrichartzHermiteQG.

BookProof.HermiteStrichartzQG.oscillator_eigenfunction (n : ℕ) (x : ℝ) : -(deriv (deriv (hermiteFun n)) x) + x ^ 2 / 4 * hermiteFun n x = oscillatorSymbol n * hermiteFun n x

Formalization note: Lean 4 identifier BookProof.HermiteStrichartzQG.oscillator_eigenfunction.

Preamble

-- Generated from ChapterStrichartzHermiteQG.lean — theorem BookProof.HermiteStrichartzQG.oscillator_eigenfunction
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterQuantumGravityDensitized
import Mathlib
import Definitions.Def_ChapterStrichartzHermiteQG
import Definitions.Def_ChapterHermiteFunctions
open BookProof.HermiteCore
open BookProof.HermiteStrichartzQG



open MeasureTheory BookProof.HermiteCore BookProof.FarisLavine
open BookProof.QuantumGravityDensitized

Formal statement

theorem BookProof.HermiteStrichartzQG.oscillator_eigenfunction (n : ℕ) (x : ℝ) :
    -(deriv (deriv (hermiteFun n)) x) + x ^ 2 / 4 * hermiteFun n x
      = oscillatorSymbol n * hermiteFun n x := by sorry

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