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Quantum tunneling is the phenomenon in which electrons say "Fuck the Police" as they break out of jail. The phenomenon is not observed in classical mechanics; because just like classical music, classical mechanics is kept clean. When electrons are presented with a barrier with a finite potential, they tunnel out in hopes to seek a better life for themselves; however, when given infinite potential, they see no need to leave the box.
This rebellious phase of the electrons is explained by wave–particle duality of matter, the electron is interested in being both a wave and a particle; just like how young people go through a experimental bisexuality phase.
The electron turns itself into a wave and bypasses the security system. Similar to how Russia hacked their way into the US 2016 Presidential Election. (But that's none of my business).
“I hate this world, I want to take me and everyone else out with me using radioactive decay.”
Quantum tunneling has always existed, it just took physicists a really long time to discover that it happens. While playing with radioactive decay in hopes to build a detonator to destroy the world, Henri Becquerel noticed that the electrons weren't "nobody's bitch" and refused to stay in the box. Becquerel also discovered, just like cats, electrons are no obedient pets.
edit Probability Function
The famous Schrodinger equation explains the probability of the position of the electron when you take the modulus squared. If the walls of the barriers have infinite potential, then the probability of the electron being in the box is 100%.
If the barriers of the walls have a finite potential, then the electron's probability of being outside the box decays as a exponential function. Get out while you still can!
Electron tunneling is used in machines such as the Scanning Tunneling Microscope. A machine in which the electrons tunnel through the material being mapped and measured by the machine. It's actually pretty cool stuff. (But I have a degree in physics, so I find every physics topic cool!)