Most physicists probably think this does not happen in reality. In [relativistic] QFT it is not possible. In non-relativistic QM there is such a non-zero probability of getting a particle to move faster than light but it is considered a failing of the theory.
Of course there is nothing surprising about a non-relativistic theory allowing faster-than-light travel - that's part of what being non-relativistic means.
Not an expert in QM.
AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order.
But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...