IndisputableMonolith.Physics.MatterWaveFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# De Broglie Matter Wave from RS — A1 QM Foundation
   6
   7De Broglie wavelength: λ = h/p = ℏ × 2π / p.
   8In RS: λ = φ^(-5) × 2π / p (since ℏ = φ^(-5)).
   9
  10Five canonical matter wave phenomena (electron diffraction, neutron diffraction,
  11atom interferometry, BEC matter wave, molecule diffraction) = configDim D = 5.
  12
  13RS prediction: de Broglie wavelength at rung k = λ₀ × φ^(-k) (decreasing).
  14
  15Lean: 5 phenomena.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Physics.MatterWaveFromRS
  21open Constants
  22
  23inductive MatterWavePhenomenon where
  24  | electronDiffraction | neutronDiffraction | atomInterferometry | BECWave | moleculeDiffraction
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem matterWaveCount : Fintype.card MatterWavePhenomenon = 5 := by decide
  28
  29noncomputable def deBroglieWavelength (k : ℕ) : ℝ := (phi ^ k)⁻¹
  30
  31theorem deBroglieDecay (k : ℕ) :
  32    deBroglieWavelength (k + 1) / deBroglieWavelength k = phi⁻¹ := by
  33  unfold deBroglieWavelength
  34  have hk := (pow_pos phi_pos k).ne'
  35  rw [pow_succ, mul_inv]
  36  field_simp [hk, phi_ne_zero]
  37
  38structure MatterWaveCert where
  39  five_phenomena : Fintype.card MatterWavePhenomenon = 5
  40  phi_decay : ∀ k, deBroglieWavelength (k + 1) / deBroglieWavelength k = phi⁻¹
  41
  42noncomputable def matterWaveCert : MatterWaveCert where
  43  five_phenomena := matterWaveCount
  44  phi_decay := deBroglieDecay
  45
  46end IndisputableMonolith.Physics.MatterWaveFromRS
  47