I am trying to learn more about quantum mechanics. I am reading a book by Griffiths that I like. I'm trying to summarize what I've learned. So below I provided three assumptions. I'd like to know if they are correct.
Consider a particle in space and time.
- We cannot know where the particle is with certainty. If we perform the same measurement experiment on an ensemble of identically prepared quantum systems, on average we may find the particle at one location more often than others.
- Under certain conditions, we can know and predict future probability distributions. Specifically, this is when the probability of the particle distribution is constant in time (eg stationary states).
- Given a probability amplitude $\Psi(x,0)$, we can predict the future value $\Psi(x,t)$ through the Schrödinger equation.
I'm pretty sure I'm misunderstanding something. In particular, No.3 suggest that I could predict future probability distributions of the wave function and I know from talking to people on SE that's wrong.
Can someone explain which (if any) of my assumptions above is wrong and explain why?