In isolated time evolution, the Schrödinger equation takes one state ψ1 to ψ2. But it does this with certainty, no? So, if one uses the standard interpretation of the inner product as probability, would that say that <ψ2 | ψ1> = 1. But this would mean that the two states are equivalent, which they aren't. So, something is wrong here. I'd be grateful to find out what.