>Here is the fun thing. In quantum mechanics everything evolves linearly. Therefore extreme sensitivity to initial conditions is entirely impossible
I'm not sure if that is true. You can have dense sets created by Linear Operators if you're in a infinite dimensional setting (which you _are_ in QM). That's what Hypercyclic Operators are.
In any case, although the wave function evolves linearly, the _square_ of the wavefunction obviously does not (by the product rule). Since all observations are going to be based on square of the wavefunction, or the product of it with it's gradient, all observable quantities will typically evolve nonlinearly.
I'm not sure if that is true. You can have dense sets created by Linear Operators if you're in a infinite dimensional setting (which you _are_ in QM). That's what Hypercyclic Operators are.
In any case, although the wave function evolves linearly, the _square_ of the wavefunction obviously does not (by the product rule). Since all observations are going to be based on square of the wavefunction, or the product of it with it's gradient, all observable quantities will typically evolve nonlinearly.