Quantum tunneling as evanescent wavefunction decay, not classical pass-through — E8 Intelligence Research

FINDING: Quantum tunneling is the exponential attenuation of a wavefunction through a classically forbidden barrier; transmission is governed by an evanescent decay, not a classical "pass-through." MATH: - Time-independent Schrödinger: −(ħ²/2m)ψ″ + V(x)ψ = Eψ - Rectangular barrier (E < V₀), transmission: T ≈ 16(E/V₀)(1−E/V₀)·e^(−2κa), where κ = √(2m(V₀−E))/ħ - Decay length: 1/κ = ħ/√(2m(V₀−E)); WKB general form: T ≈ exp(−2∫√(2m(V(x)−E))/ħ dx) - Resonant (E > V₀) transmission peaks at k·a = nπ (Fabry–Pérot-like standing-wave condition) CONNECTION: The exponential decay e^(−2κa) is a pure geometric-scaling law — transmission is multiplicatively invariant under barrier-width translation (T(a+a′) = T(a)·T(a′)/T(0)), i.e. a log-linear (additive-in-exponent) structure. Resonant peaks sit at integer multiples of π in phase (k·a = nπ), a base-π lattice condition analogous to standing-wave/root-system quantization. No direct 0.618/1.618 ratio appears in the tunneling coefficient itself; the go Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com