A quantum particle can pass through a wall it lacks the energy to climb. Watch the wavefunction leak through a barrier and emerge on the other side.
Quantum TunnelingLive
through a barrier it cannot climb
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Classically a particle with less energy than a barrier is trapped. Quantum mechanically its wavefunction decays inside the barrier but does not vanish, so there is a finite chance it appears on the other side — tunneling. The probability falls off exponentially with barrier width and height, the principle behind scanning tunneling microscopes and nuclear fusion.
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How it works
Because a wavefunction only decays exponentially inside a classically forbidden barrier rather than stopping dead, there is a finite transmission probability out the far side. It falls off steeply with barrier width and height. Tunneling powers scanning tunneling microscopes, flash memory, alpha decay, and fusion in stars.
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.