A quantum wave packet impinging on a potential barrier. Even when the particle energy is below the barrier height, there is a nonzero probability of transmission — quantum tunneling.
2.0
1.5
1.2
1.5
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Transmission T
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Reflection R
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E/V₀
T = |t|² where t = [cosh(κa)+i(κ²-k²)sinh(κa)/(2kκ)]⁻¹, κ=√(2m(V₀-E))/ℏ. Exponential decay through evanescent wave inside barrier.