According to my understanding of things, the time evolution operator in QM looks something like this,
$$U = \exp(-iHt/\hbar)$$
Which acts on the state vector / wave-function of the system to effectively step forward in time.
I notice that this is a unitary operator. Given that one of the postulates of quantum mechanics is that two states are identical if they differ only by a phase factor (a unitary complex scalar?), then surely this operation does not actually change the state of the system?
Am I missing something here?