Probability Wave Function Ψ(r,t): Time Independence

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Wave function Ψ(r,t) is time dependent. But then why probability [Ψ(r,t)]2 is time independent
 
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It isn't.
 
Sometimes it is, when psi(x,t) is an energy eigenstate. (I hope I don't need to explain why.)
 
Demystifier said:
Sometimes it is, when psi(x,t) is an energy eigenstate. (I hope I don't need to explain why.)

Oh, I thought the question was intended in more general terms.
 

Thread 'Is a table levitating possible, even at a minuscule probability?'

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...
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