Originally Posted by **neila9876** "...Most of Introductory level QM deals with Linear Algebra at its base concepts. Along with that concept comes "linear superposition," which means that we can simply add the wavefunctions as they move with respect to each other.
No, waves cannot be considered to be a sum of particle states.
This is exactly what I mean. You need more information to talk about QM. I could make a list if you like. I'd suggest starting with Linear Algebra.
What I've seen of X4 is that it illuminates nothing but obscures the structure that is there. (And in QM we don't need more complexities!)"
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The biggest misconcept is: math superior to physics |

If you have waves that obey the superposition principle then QM is greatly simplified. And many of the waves we observe are, to a large degree, linear. However, it is true that much of Physics does tend to work with linear waves because the Math of non-linear behavior is much more complicated. In that sense Physicists are a bit blind when it comes to non-linear behavior.

Of course we need to have more information to talk about QM. If we could find a method to understand everything (or at least a lot of) about QFTs then we'd be in a much better situation.

I have a tendance to joke about Physics being better than Math but when it comes down to it Math is the major tool that Physics uses to understand what is going on (at least from the standpoint of Theoretical Physics, which is primarily what I do.)

-Dan