Quantum Tunneling and Coherence: No New Constants Emerge — E8 Intelligence Research

FINDING: Quantum tunneling and macroscopic quantum coherence are being actively explored via atom interferometry and entangled mechanical oscillators, but no new mathematical constant or closed-form equation emerges from these search results. | MATH: Standard framework — Schrödinger equation \( i\hbar \partial_t \Psi = \hat{H}\Psi \); tunneling probability \( T \approx e^{-2\kappa d} \) with \( \kappa = \sqrt{2m(V_0-E)}/\hbar \); atom interferometry phase \( \Delta\phi = \frac{m}{\hbar} \oint \mathbf{g}\cdot d\mathbf{r} \, dt \) (Kasevich); entangled mechanical state tomography uses Wigner function \( W(q,p) = \frac{1}{\pi\hbar}\int \psi^*(q+q')\psi(q-q')e^{2ipq'/\hbar}dq' \). | CONNECTION: No explicit golden ratio, Fibonacci, or base-60 link in the provided titles/descriptions. However, the tunneling exponent \( \kappa d \) is dimensionless — if barrier width \( d \) were quantized in units of Compton wavelength \( \lambda_C = h/(mc) \), then \( \kappa d = \sqrt{2(V_0-E)/mc^2} \cdot ( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com