Quantum Tunneling: Wave-Mechanical Barrier Penetration and Relativistic Limits — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-14
DOI
https://doi.org/10.5281/zenodo.22748143
Primary Topic
Quantum Mechanics and Non-Hermitian Physics
Type
preprint
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preprint

Quantum Tunneling: Wave-Mechanical Barrier Penetration and Relativistic Limits — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Non-Hermitian Physics
preprint

Quantum Tunneling: Wave-Mechanical Barrier Penetration and Relativistic Limits — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, governed by exponential decay of the wavefunction inside the barrier; "impossible" QFT measurements are possible but non-ideal, with relativistic causality constraints. MATH: Transmission coefficient \(T \approx e^{-2\kappa L}\), where \(\kappa = \sqrt{2m(V_0-E)}/\hbar\); barrier penetration probability \(P \propto e^{-2\int \kappa(x)dx}\). For a rectangular barrier: \(T = \left[1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}\right]^{-1}\). In the WKB limit, \(T \sim \exp\left(-\frac{2}{\hbar}\int_{x_1}^{x_2}\sqrt{2m(V(x)-E)}\,dx\right)\). No new fundamental constants emerge; the key is the exponential suppression factor. CONNECTION: The exponential decay \(e^{-\kappa L}\) has no direct golden-ratio link. However, the *critical* barrier opacity \(\kappa L = \ln(2)\) (for 50% transmission) and \(\kappa L = \ln(\phi) \approx 0.4812\) (where \(\phi = 1.618...\)) appear as natural thresholds — but t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Non-Hermitian Physics
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Quantum Tunneling: Wave-Mechanical Barrier Penetration and Relativistic Limits — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS