An electron runs at a wall it doesn't have the energy to climb. A ball would bounce back every time. The electron's wave leaks into the wall, and some of it comes out the other side.
Energy is below the barrier, so a classical ball always bounces back.
The blue hump is |ψ|², the probability of finding the electron at each spot. It starts as one lump moving right at a definite average energy. The amber block is a region where the electron would need more energy than it has.
This is a live solution of the Schrödinger equation on 2,048 grid points, stepped forward every 0.02 femtoseconds. When the packet hits the barrier, it splits. The bar underneath tallies how much probability ended up on each side, and the white tick shows what the textbook formula predicts.
Inside the barrier the electron's kinetic energy would be negative, which is impossible for a ball. For a wave it just means the wave stops oscillating and fades instead. If the wall is thin enough, the wave hasn't faded to nothing by the far side, and there it carries on as a normal travelling wave.
Each electron is detected whole, on one side or the other. Nobody ever catches one halfway through. The percentages are odds for single electrons.
Tunneling is not a lab curiosity. It keeps the Sun burning, decides how long radioactive atoms last, and runs through the electronics in your pocket.
A sharp metal tip hovers a few atom-widths above a surface, and electrons tunnel across the vacuum gap. The current falls about tenfold for every extra 0.1 nm of gap, so it maps individual atoms. Binnig and Rohrer built it at IBM Zurich in 1981.
In the demo: nudge the width slider and watch transmission swing by large factors.Each bit in a USB stick or phone's storage is charge trapped behind a thin insulating layer. A strong voltage thins the barrier enough for electrons to tunnel in or out, which is how bits are written and erased. With the voltage off, the charge stays put for years.
In the demo: a thick, high barrier holds almost everything back.The Sun's core is about 15 million kelvin, far too cool for two protons to overcome their electric repulsion by brute force. They fuse because they tunnel through it. Without tunneling the Sun would not shine.
In the demo: the classical ball never makes it; the wave sometimes does.An alpha particle is trapped inside a nucleus by a barrier it can't climb. In 1928 Gamow, and separately Gurney and Condon, explained its escape as tunneling. Because the odds depend exponentially on energy, half-lives range from under a microsecond to billions of years.
In the demo: small changes in energy make big changes in transmission.Leo Esaki's 1957 tunnel diode passes current by tunneling through a very thin junction, giving it switching speeds used in high-frequency oscillators. Josephson junctions, where pairs of electrons tunnel between superconductors, are the building block of many quantum computers.
In the demo: a barrier under a nanometre thick lets a lot through.Some enzymes move hydrogen atoms faster than classical chemistry allows. Swapping hydrogen for heavier deuterium slows soybean lipoxygenase about 80 times, far beyond the classical limit of around 7, a sign that the hydrogen tunnels.
In the demo: a heavier particle fades inside the barrier as if the barrier were higher.