Quantum tunneling is a good, specific example. It is not predicted by classical mechanics. If I have a particle which is bound inside a potential well, say an

Quantum tunneling is a good, specific example. It is not predicted by classical mechanics. If I have a particle which is bound inside a potential well, say an electron which is part of an atom, by virtue of being electrically attracted to the atom's nucleus, from time to time it can escape the potential well. Say for example I have a hydrogen atom, with an electron and a proton, and a positively-ionized hydrogen atom - that's actually just a bare proton. From time to time the electron will bind to the other proton, without appearing to cross the space in-between.