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Quantum Mechanics - I PHYS 4307 V0 Syllabus

Nural Akchurin, Eugen Merzbacher

Published Jan 1, 2009• 0 citations
OpenAlex

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FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, not a classical "jump"; its probability depends exponentially on barrier width and height, with no known teleportation mechanism. | MATH: Transmission coefficient \(T \approx e^{-2\kappa L}\), where \(\kappa = \sqrt{2m(V_0-E)}/\hbar\); for a rectangular barrier, exact \(T = [1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}]^{-1}\). No new constants or ratios emerge beyond \(\hbar\), \(m\), \(V_0\), \(E\), \(L\). | CONNECTION: The exponential decay \(e^{-2\kappa L}\) has no direct ratio to 0.382/0.618/1.618; however, the *critical* condition \(E = V_0\) yields \(\kappa = 0\) and \(T \to 1\) (resonant transparency), which is a phase-transition-like threshold — analogous to a golden-ratio bifurcation point in some dynamical systems, but not evidenced here. No crystallographic or base-60 link. | DEPTH: 3 — Standard quantum mechanics, well-understood; the "impossible measurements" QFT paper (arXiv:2311.13 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, not a classical "jump"; its probability depends exponentially on barrier width and height, with no known teleportation mechanism. | MATH: Transmission coefficient T≈e−2κLT \approx e^{-2\kappa L}T≈e−2κL, where κ=2m(V0−E)/ℏ\kappa = \sqrt{2m(V_0-E)}/\hbarκ=2m(V0​−E)​/ℏ; for a rectangular barrier, exact T=[1+V02sinh⁡2(κL)4E(V0−E)]−1T = [1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}]^{-1}T=[1+4E(V0​−E)V02​sinh2(κL)​]−1. No new constants or ratios emerge beyond ℏ\hbarℏ, mmm, V0V_0V0​, EEE, LLL. | CONNECTION: The exponential decay e−2κLe^{-2\kappa L}e−2κL has no direct ratio to 0.382/0.618/1.618; however, the *critical* condition E=V0E = V_0E=V0​ yields κ=0\kappa = 0κ=0 and T→1T \to 1T→1 (resonant transparency), which is a phase-transition-like threshold — analogous to a golden-ratio bifurcation point in some dynamical systems, but not evidenced here. No crystallographic or base-60 link. | DEPTH: 3 — Standard quantum mechanics, well-understood; the "impossible measurements" QFT paper (arXiv:2311.13 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com