Why must Schrödinger's equation be linear?

[UrbanXrisis]

I was wondering if someone could explain to me why is Schrödinger's Equation has to be linear?

 

[Ratzinger]

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.

 

[topsquark]

I was wondering if someone could explain to me why is Schrödinger's Equation has to be linear?

I can't say anything intelligent about it because I've never studied it, but there IS a non-linear Schrödinger's equation. You could probably Google it.

-Dan