WKB structure in a variable-coefficient forbidden region

TWKB names the first-order approximation, not exact T for any barrier; C₀ is an integration constant. Preserve divergence form and interface ψ,bψ′; require |κ′|/κ²≪1 and |b′|/(bκ)≪1, with turning-point matching.

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Based on the final manuscript · Chapter 5

ASD-WEB-QM-033

\kappa(x)=\sqrt{\frac{2m_0[V(x)-E]}{\hbar^2b(x)}},\quad A(x)=\frac{C_0}{\sqrt{b(x)\kappa(x)}},\quad T_{\rm WKB}=\mathcal P\exp\!\left[-2\int_{x_1}^{x_2}\kappa(x)dx\right]

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ASD-WEB-QM-033 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

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Ch. 5 (5.3.37)–(5.3.39)

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Selected channel and stated initial/boundary conditions; action/energy matching retained
Continuum, slow-envelope and detector approximations kept at their respective levels

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Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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QM-0accdcbe7725 · Ch. 5 (5.3.37)–(5.3.39)

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