Does the Schrödinger equation link position and momentum?

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Discussion Overview

The discussion revolves around the relationship between the Schrödinger equation, average position, and average momentum in quantum mechanics. Participants explore the implications of the equation and its connection to classical mechanics, as well as the challenges in understanding these concepts, particularly regarding wave functions and superposition.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant expresses confusion about how the Schrödinger equation links average position and average momentum, despite being able to prove it mathematically.
  • Another participant questions how to derive the Schrödinger equation and notes that the wave function contains information necessary to calculate expected values of position and momentum.
  • A third participant critiques the author of an article for lacking fundamental understanding of the subject, suggesting that they should read more authoritative texts on classical mechanics and quantum theory.
  • Another participant agrees with the critique, emphasizing that the question posed by the article is too basic for a proper understanding of quantum mechanics.

Areas of Agreement / Disagreement

Participants generally express disagreement regarding the quality of the article in question and the author's understanding of quantum mechanics. There is no consensus on the clarity of the relationship between the Schrödinger equation and the concepts of position and momentum.

Contextual Notes

Some participants highlight the need for a deeper understanding of classical mechanics and quantum theory to fully grasp the implications of the Schrödinger equation, indicating potential limitations in the article's explanations.

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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Likes   Reactions: vanhees71 and drvrm

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