Does the Schrödinger equation link position and momentum?

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SUMMARY

The discussion centers on the relationship between the Schrödinger equation and the concepts of average position and momentum in quantum mechanics. Participants highlight that the average position can be derived from the average momentum, aligning with classical mechanics principles. However, there is confusion regarding the fundamental reasons behind this relationship and the concept of superposition of momenta. The need for a deeper understanding of wave functions and their solutions to the Schrödinger equation is emphasized, along with the suggestion to consult foundational texts in classical mechanics and quantum theory.

PREREQUISITES
  • Understanding of the Schrödinger equation in quantum mechanics
  • Familiarity with wave functions and their properties
  • Knowledge of classical mechanics principles
  • Basic concepts of superposition in quantum systems
NEXT STEPS
  • Study the derivation of the Schrödinger equation in quantum mechanics
  • Explore the mathematical formulation of wave functions and their solutions
  • Research the concept of superposition of momenta in quantum systems
  • Read foundational texts on classical analytical mechanics and quantum theory
USEFUL FOR

Students of quantum mechanics, physicists exploring wave-particle duality, and anyone seeking to understand the foundational principles linking position and momentum in quantum systems.

AuxPart
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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 :oldsmile:
 
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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.
 
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!
 
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AuxPart said:
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.
 
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