Eigenvectors associated with distinct values of an observable are orthogonal, according to quantum mechanics.
Does this entail that a quantum system cannot continuously evolve from one eigenstate into another, for ANY observable?
At first, that seems strange: it seems like a particle should be able to "travel" in the sense of continuously moving from one eigenstate of position to the next.
Another example: can't a particle "speed up" (i.e. go continuously go from one velocity eigenstate to the next)?