QUANTUM TUNNELLING

Two protons in the Sun’s core lack the energy to clear the Coulomb barrier, yet the Sun burns anyway, because now and then they pass through the barrier instead of over it. Transmission falls off exponentially with barrier width, so a slightly thicker barrier sends the tunnelling probability off a cliff while the reflected wave takes almost everything. The same arithmetic covers both the alpha decay of a uranium nucleus and the current crossing the vacuum gap under a scanning tunnelling microscope tip.

▸ Building the rectangular potential barrier (height V₀ · width a)…
▸ Initialising the wave packet |ψ|² & particle energy level E
▸ Computing the decay constant κ = √(2m(V₀−E))/ħ
▸ Splitting the reflected wave ◀ and transmitted wave ▶ (T + R = 1)
▸ Loading applications: alpha decay · STM · stellar fusion
▸ Ready — Online. ✅
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⌂ Particles & Quantum

Simulation room Quantum Tunnelling

Quantum Tunneling
Online
wave packet · barrier · T~e^(−2κa) · alpha · STM
Current scenario
⛰️ Rào vừa
Particle energy E—
Barrier height V₀—
Barrier width a—
Decay constant κ—
Transmission T—
Reflection R—
Quantum note
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A wave packet arrives from the left and hits the potential barrier → part reflects, part tunnels through even though E<V₀ · adjust E · V₀ · width a on the right
Transmission T / reflection R over time T (tunnelled)R (reflected)
About Quantum Tunneling

Two protons in the Sun’s core lack the energy to clear the Coulomb barrier, yet the Sun burns anyway, because now and then they pass through the barrier instead of over it. Transmission falls off exponentially with barrier width, so a slightly thicker barrier sends the tunnelling probability off a cliff while the reflected wave takes almost everything. The same arithmetic covers both the alpha decay of a uranium nucleus and the current crossing the vacuum gap under a scanning tunnelling microscope tip.

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