Quantum Tunneling: Exponential Wavefunction Leakage and Transmission Probability — E8 Intelligence Research

FINDING: Quantum tunneling is the exponential leakage of a wavefunction through a classically forbidden barrier; the transmission probability is dominated by an exponential decay set by barrier width and the particle's evanescent decay constant. | MATH: For a rectangular barrier of height V₀ and width a, with E < V₀: T ≈ 16(E/V₀)(1−E/V₀)·e^(−2κa), where κ = √(2m(V₀−E))/ħ. Decay length 1/κ. WKB generalization: T ≈ exp(−(2/ħ)∫√(2m(V(x)−E))dx). | CONNECTION: No direct geometric-harmony ratio in the tunneling formula itself. The exponential e^(−2κa) is a scaling law, not a φ-ratio. However, resonance conditions in double-barrier (resonant tunneling) structures occur at discrete energies satisfying a phase-quantization condition 2ka + 2φ = 2πn — a standing-wave/lattice-quantization structure analogous to crystallographic Bragg conditions. | DEPTH: 7 FINDING: Quantum annealing exploits tunneling through barriers in an energy landscape to solve discrete combinatorial optimization problems. | Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com