Hello, we started Quantum Mechanics last semester, and somehow I manged to do most of the homework during that semester, but now I'm trying to revise it again, and I can't seem to understand the very basics of it, in particular about wavefunctions. Please read this carefully, because you might not understand where the confusion is (I tried Physics chat room, but no-one seemed to understand what i was saying, just saying that I was wrong, and all of it is complete nonsense) At first I thought that there is like a general wavefunction, that is something abstract that changes with time(like e.g. we know what rotation does, but the rotation matrix looks differently in different bases) so i thought a wave function is like a function of infinitely many variables, e.g. x-positing, p-momentum, spin, energy... and we need to "project" it on one of those bases <x|psi(t)> = psi (x, t) (so this step is like representing a rotation with a matrix in a basis). And then we are working in one of those bases (position), I can do other stuff now, like find probabilities amplitudes that it's in some state q using : <q | psi (x,t)> and do other find expected values etc... But after reading Griffiths introduction to quantum mechanics for a bit, I realized that my logic is probably wrong. So I started thinking again. As I understand now, a general wavefunction is like a vector space of infinitely many square integrable functions (and their linear combinations and stuff are obviously in that vector space as well), so it's just like a database of infinitely many functions, which are all functions of x and t (in 1 dimension). And so now, we just take this wavefunction and take scalar product with state vectors that we are interested in straight away, <q | psi(x,t)> and we'll get the probability amplitude. Is that correct? I'm a bit confused because states are vectors, can you give some examples of states? can a state be a function (e.g. q is some function, of what variables?) then obviously <q (...) | psi (x,t)> = integral q*psi(x,t)dx or something. Thanks in advance p.s. At our lectures, we were actually never told what a wavefunction is, our lecturer thought it made more sense to start with Probability Amplitudes and assume that everyone knows what a wavefunction means.