The Logical Cost of Quantum Tunneling: LLPO and WKB Turning Points

Paper 19: WKB Tunneling and LLPO Title: The Logical Cost of Quantum Tunneling: LLPO and WKB Turning Points Description:Paper 19 in the Constructive Reverse Mathematics (CRM) of Mathematical Physics series. This paper establishes the first physical calibration at LLPO (Lesser Limited Principle of Omniscience), filling the gap between BISH and WLPO. The formalization decomposes quantum tunneling into three tiers: Part A (BISH) shows that for polynomial barriers with explicitly known turning points, the WKB tunneling amplitude is fully computable; Part B (LLPO) proves that for general continuous barriers, the existence of classical turning points x₁, x₂ satisfying V(x) = E is equivalent to LLPO via the Intermediate Value Theorem; Part C (LPO) demonstrates that the full semiclassical limit ℏ → 0 requires LPO. A key insight is that the non-constructivity lies in classical geometry (locating turning points), not in quantum mechanics itself. Lean 4 formalization (Mathlib, v4.28.0-rc1): 1,081 lines, 0 errors, 0 warnings, 0 sorry. Keywords: constructive reverse mathematics, quantum tunneling, WKB approximation, LLPO, turning points, intermediate value theorem, semiclassical limit, Lean 4, Mathlib Complete Paper List Other papers in the Constructive Reverse Mathematics Series (see Zenodo for current files): Paper 1: WithdrawnPaper 2: Bidual gap and WLPO — DOI: 10.5281/zenodo.17107493Paper 3: WithdrawnPaper 4: Quantum spectra axiom calibration — DOI: 10.5281/zenodo.17059483Paper 5: Schwarzschild curvature verification — DOI: 10.5281/zenodo.18489703Paper 6: Heisenberg uncertainty (v2, CRM over Mathlib) — DOI: 10.5281/zenodo.18519836Paper 7: Physical bidual gap, trace-class operators — DOI: 10.5281/zenodo.18527559Paper 8: 1D Ising model and LPO — DOI: 10.5281/zenodo.18516813Paper 9: Ising formulation-invariance — DOI: 10.5281/zenodo.18517570Paper 10: Logical geography of mathematical physics — DOI: 10.5281/zenodo.18580342 v 2.0 Technical Synthesis of Papers 1–16Paper 11: Entanglement, CHSH, Tsirelson bound — DOI: 10.5281/zenodo.18527676Paper 12: Constructive history of mathematical physics — DOI: 10.5281/zenodo.18581707 v 2.0 Historical Synthesis of Papers 1–16Paper 13: Event horizon as logical boundary — DOI: 10.5281/zenodo.18529007Paper 14: Quantum decoherence — DOI: 10.5281/zenodo.18569068Paper 15: Noether theorem — DOI: 10.5281/zenodo.18572494Paper 16: Technical note: Born rule — DOI: 10.5281/zenodo.18575377Paper 17: Bekenstein-Hawking formula — DOI: 10.5281/zenodo.18597306Paper 18: Fermion mass hierarchy and scaffolding principle — DOI: 10.5281/zenodo.18600243Paper 19: WKB tunneling and LLPO — DOI: 10.5281/zenodo.18602596Paper 20: Observable-dependent logical cost, 1D Ising magnetization and WLPO — DOI: 10.5281/zenodo.18603079Paper 21: Bell nonlocality and LLPO — DOI: 10.5281/zenodo.18603251Paper 22: Markov's Principle and radioactive decay — DOI: 10.5281/zenodo.18603503 Note: GitHub repository is not maintained; please see Zenodo for current files.