I am confused about what I think should be the most basic concepts in quantum mechanics.. As far as I understood, a system that can be in only one of two states, can literally be only in one of those two states, right? So if I were to make a hypothetical measurement of the configuration of that system, I could only get one of those states as a result of that measurement (and never something in between, mostly because there is nothing in between). But then there is the idea of the superposition of those states. Which implies that my system can abstractly be in one of these non-existent states. I will never get one of those as a result of an experiment, but it reflects my uncertainty of the state of that system in a particular instant in time, right? I guess my confusion starts with the motivation of inventing these in-between states. Is it because my system's time evolution is probabilistic? So even though I may choose to start it at some realizable state, in a couple of seconds I might only be able to predict the state of that system up to a probabilistic result? So would the bottom line be: in classical mechanics I can just say that in three seconds from now your system is going to be in the state X. In quantum mechanics I don't want to say "I don't know", so I just say in three seconds from now your system is going to be in the "state" of having 30% probability of being in state X and 70% probability of being in state Y? Than my final question is why do we use probability amplitudes to talk about these states rather than just straight up probability?