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.
 

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