As a beginner in QM, all the video lectures that i have seen talk about superposing wave functions in order to get $\psi$. But from what i know from linear algebra, the system must be linear in order for us to do this superposition.
So, what tells us that quantum systems are linear systems? Does it come out of experimental results or from some intuitive physical explanation? If it's the first, then if we treat all quantum mechanical systems as linear, how can we find a non-linear system that might exist but has not been seen in labs yet? (I mean that in this way we exclude all possibilities that a non linear quantum system might exist). If it's the second, then can you give me that intuitive explanation?
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