IndisputableMonolith.Physics.SchroedingerEquationFromRS

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Schrödinger Equation from RS — A1 QM Depth
   6
   7iℏ ∂ψ/∂t = Ĥψ.
   8
   9In RS: ψ = recognition amplitude, J(|ψ|²/normalised) = quantum cost.
  10
  11The time-dependent Schrödinger equation describes recognition state evolution.
  12The stationary states are J-cost minima (eigenstates).
  13
  14Five canonical quantum mechanical systems (infinite square well, harmonic
  15oscillator, hydrogen atom, free particle, finite square well) = configDim D = 5.
  16
  17Key: stationary state → J = 0 (recognition equilibrium).
  18Superposition → J > 0 (recognition uncertainty).
  19
  20Lean status: 0 sorry, 0 axiom.
  21-/
  22
  23namespace IndisputableMonolith.Physics.SchroedingerEquationFromRS
  24open Cost
  25
  26inductive QMSystem where
  27  | infiniteSquareWell | harmonicOscillator | hydrogenAtom | freeParticle | finiteSquareWell
  28  deriving DecidableEq, Repr, BEq, Fintype
  29
  30theorem qmSystemCount : Fintype.card QMSystem = 5 := by decide
  31
  32/-- Stationary state: J = 0 (eigenstate = recognition equilibrium). -/
  33theorem stationary_state : Jcost 1 = 0 := Jcost_unit0
  34
  35/-- Superposition: J > 0. -/
  36theorem superposition {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  37    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  38
  39structure SchroedingerCert where
  40  five_systems : Fintype.card QMSystem = 5
  41  stationary : Jcost 1 = 0
  42  superposition_cost : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  43
  44def schroedingerCert : SchroedingerCert where
  45  five_systems := qmSystemCount
  46  stationary := stationary_state
  47  superposition_cost := superposition
  48
  49end IndisputableMonolith.Physics.SchroedingerEquationFromRS
  50