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Galileo

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Take a particle and consider the state space. And let's call, say, the first tree stationary states [itex]|\psi_1 \rangle, |\psi_2 \rangle, |\psi_3 \rangle[/itex].

The question is:

Is there ANY (physical) difference between saying:

"There is a 1/3 probabilty the particle is in the state [itex]|\psi_1 \rangle[/itex], a 1/6 probability it's in the state [itex]|\psi_2 \rangle[/itex] and a prob. of 1/2 that it's in the state [itex]|\psi_3 \rangle[/itex]."

and saying

"The particle is in the state

[tex]\frac{1}{\sqrt{3}}|\psi_1 \rangle+\frac{1}{\sqrt{6}}|\psi_2 \rangle+\frac{1}{\sqrt{2}}|\psi_3 \rangle[/tex]"

I'm pretty sure the answer is no, since any physical measurement will give the same predictions in both cases. Unless I missed something.

Can someone answer this question?

(Preferrably someone ho knows what he's talking about).