Does the Schrödinger equation link position and momentum?

[AuxPart]

I recently found this article about the dynamics of the wave function. It has some good simple illustrations and I found it valuable. But the author has a question himself, about understanding the Schrödinger equation. I wonder if anybody here could fill in the missing piece. The relevant part is:

From the Schrödinger equation can be derived the fact that the average position varies according to the average momentum. This coincides with the classical setting of classical mechanics! This should sound surprising to you. At least, it does to me. Even though I can prove it mathematically, I have no understanding of the fundamental reason why Schrödinger equation links average position and average momentum.

In particular, I can’t seem to find a way to relate Schrödinger equation with the idea of superposition of momenta. This prevents me from describing the spreading of position through time. If you find a way to combine my representations of wave functions with Schrödinger equation and the ideas of superposition, I would be very interested in hearing about it!

I'm not sure if the topic of this thread is the best choice, but I think it's what I want to ask

 

[drvrm]

From the Schrödinger equation can be derived ...i wonder how to derive Schrödinger equation?

regarding the definition of position and momentum...
the wavefunction carries the info and the expected value of position and momentum

can be calculated if one has 'the wave function' which are solutions of Schrödinger equation.

 

[vanhees71]

Well, then the author should read good textbooks on classical analytical mechanics and then on quantum theory, before writing about a subject he obviously doesn't understand in its very fundamentals himself :-((. I'm not sure, whether I should read his blog, given that he isn't aware of the very fundamentals!

 

[PeterDonis]

the author has a question himself

Which is such a basic question that I have to agree with @vanhees71 , this article is not a good source for learning about QM.