I was wondering if someone could explain to me why is Schrodinger's Equation has to be linear?
It has to be linear so that also linear combinations of solutions are also solutions of the Schrödinger equation. Quantum states as represented by state vectors ( wave functions in position space) are superposed states, i.e. linear combinations of vectors with complex numbers as their components.
So the superposition principle needs it to be linear.
I can't say anything intelligent about it because I've never studied it, but there IS a non-linear Schrodinger's equation. You could probably Google it.
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