Quantum Tunneling: Exponential Attenuation via Evanescent Decay, Not Classical Trajectories — 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 constant, not a classical trajectory. | MATH: T ≈ exp(−2κL), κ = √(2m(V₀−E))/ℏ. Barrier width L, height V₀, energy E. WKB: T ≈ exp[−(2/ℏ)∫√(2m(V(x)−E))dx]. | CONNECTION: Exponential decay is scale-invariant (no preferred length); no direct 0.618/1.618 ratio appears. However, resonant tunneling in a double barrier produces transmission peaks at discrete energies — a Fabry–Pérot-like condition kL = nπ, which is a harmonic (integer) quantization, not golden-ratio. | DEPTH: 6 FINDING: Quantum annealing exploits tunneling to traverse energy barriers that classical thermal annealing cannot cross, mapping combinatorial optimization onto an Ising Hamiltonian. | MATH: H = −Σ Jᵢⱼσᵢᶻσⱼᶻ − Σ hᵢσᵢˣ (transverse-field Ising). Tunneling amplitude Γ drives transitions between local minima; gap Δ between ground and first excited state deter Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com