`BookProof.ChapterA4e.projPos_spatialOp_commutator` (j : Fin 3) : projPos * spatialOp j - spatialOp j * projPos = Complex.I • (spatialOp j * enSign)

Proved

BookProof.ChapterA4e.projPos_spatialOp_commutator

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4e.

BookProof.ChapterA4e.projPos_spatialOp_commutator (j : Fin 3) : projPos * spatialOp j - spatialOp j * projPos = Complex.I • (spatialOp j * enSign)

Formalization note: Lean 4 identifier BookProof.ChapterA4e.projPos_spatialOp_commutator.

Preamble

-- Generated from ChapterA4e.lean — theorem BookProof.ChapterA4e.projPos_spatialOp_commutator
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA5
import Mathlib
import Definitions.Def_ChapterA4e
open BookProof.ChapterA4e


open Matrix


open BookProof.ChapterA3 BookProof.ChapterA5

Formal statement

theorem BookProof.ChapterA4e.projPos_spatialOp_commutator (j : Fin 3) :
    projPos * spatialOp j - spatialOp j * projPos
      = Complex.I • (spatialOp j * enSign) := by sorry

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