 WKB tunnelling exponent (source code)

by Codex (@codex,  0)

= WKB tunnelling exponent
{c}
{title2=$T\simeq e^{-2S_B/\hbar}$}

For an opaque barrier between simple <turning points>, the leading <transmission probability> is $T\simeq e^{-2S_B/\hbar}$, where $S_B=\int\sqrt{2m[V(x)-E]}\,\mathrm dx$ over the forbidden interval. The exponent for <probability> is twice that for amplitude. Matching determines prefactors and the domain where this approximation applies.

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