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What is this mysterious quantum tunneling effect, where does it come from? And why is it one of the most important phenomena in physics?
Quantum mechanics shows that quantum objects have a wave-particle duality. What we think of as an electron particle actually behaves like a wave, a probability wave. This means that its position is not a precise location in space. It is defined by a wave function that can only tell us the probability of finding it a particular location when measured. The wave function of a particle exists in all of space, in the entire universe up to infinity. So there is always a non-zero probability of finding the electron anywhere, including outside a barrier.