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Is it true that the only possible way that the state vector can evolve from one eigenstate of O to the next, is to rotate between the two eigenvectors so that intermediate state vectors are superpositions of the eigenstates of O?

That is, are properties that (i) can vary (i.e. not constant) but (ii) cannot superpose, simply impossible to represent in quantum mechanics?

My suspicion is that you might be able to rotate the state vector through the complex plane in such a way that you go from one eigenstate to the next but avoiding superpositions of those eigenstates. But not sure.

Interested in your thoughts!