Barrier transmission coefficient and conserved flux

Exact boundary solution for equal exterior parameters, real potential and 0<E<V₀. z,D abbreviate 5.3.34; Rrefl is reflectance, not core radius. Complex exponential superposition carries flux.

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ASD-WEB-QM-031

\begin{aligned}T&=\left[1+\frac{V_0^2\sinh^2(\kappa a)}{4E(V_0-E)}\right]^{-1},\\ z&=e^{-2\kappa a},\quad D=V_0^2(1-z)^2+16E(V_0-E)z,\\ T&=\frac{16E(V_0-E)z}{D},\quad R_{\rm refl}=\frac{V_0^2(1-z)^2}{D},\quad T+R_{\rm refl}=1,\\ j_{\rm II}&=\frac{2\hbar\kappa}{m_0}\operatorname{Im}(AB^*)\end{aligned}

Exact boundary solution for equal exterior parameters, real potential and 0<E<V₀. z,D abbreviate 5.3.34; Rrefl is reflectance, not core radius. Complex exponential superposition carries flux.
Chapter reference: Ch. 5 (5.3.32)–(5.3.35) · ASD-BOOK-ddbade997b45

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Ch. 5 (5.3.32)–(5.3.35)

Exact boundary solution for equal exterior parameters, real potential and 0<E<V₀. z,D abbreviate 5.3.34; Rrefl is reflectance, not core radius. Complex exponential superposition carries flux.

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QM-0accdcbe7725 · Ch. 5 (5.3.32)–(5.3.35)

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