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.
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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