3 ms·
As your link shows, the time evolution of the expectation value of position does in fact not generally obey a closed-form non-linear differential equation; inst
by prof-dr-ir 6y ago
As your link shows, the time evolution of the expectation value of position does in fact not generally obey a closed-form non-linear differential equation; instead one needs the expectation value of V'(x) which is a different quantity altogether. But the easiest way to compute that quantity is of course to solve the Schrodinger equation...
Edit: removed an accusation because I misread the original comment.
- pontus 6y agoYes, that's right: you need <V'(x)> rather than V'(<x>). It's still the case that <x> does not follow a linear DE. My point was that while the SE is linear, that does not mean that everything derived from it is also linear. The original comment was asking where all the nonlinearities in the world could come from since the SE is linear. It was suggested that either QM is incomplete because it is linear or that we need wave function collapse to introduce nonlinearities. I think my counterexample shows that both of those suggestions are incorrect.