Parameters
Presets
Particle type
Barrier height V₀5.0 eV
Barrier width a1.00 nm
Particle energy E2.0 eV
Double barrier (resonance)
Barrier separation d2.0 nm
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Tunneling prob. T [%]
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Decay const. κ [nm⁻¹]
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Penetration depth [nm]
—
de Broglie λ [nm]
Key Formulas
E < V₀ (below barrier):
$$\kappa = \frac{\sqrt{2m(V_0-E)}}{\hbar}, \quad T_{WKB} \approx e^{-2\kappa a}$$Transfer matrix (exact):
$$T = \left[1 + \frac{(k^2+\kappa^2)^2}{4k^2\kappa^2}\sinh^2(\kappa a)\right]^{-1}$$Resonance condition (E > V₀): $k'a = n\pi$ → T=1
Applications: Alpha decay (Geiger-Nuttall law) / Tunnel diode negative resistance / STM atomic-resolution imaging / Ammonia inversion microwave maser.