Particles in an energy eigenstate not moving?

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sheelbe999
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I'm really struggling with this one guys, the question is:

Explain why a particle which is in an energy eigenstate cannot be moving in the
classical sense.
 
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What you need to know to answer this is a) the interpretation of a wavefunction, and b) how a wavefunction changes with time. (If you know that the state at t=0 is f, then what is it at arbitrary t? f(t)=(something)f, right?).

(This should probably be in the homework forum).
 
Hints: This has to do with "stationary states".

What is a prerequisite for a stationary state? What do stationary states imply for expectation values?