Does the Schrödinger equation link position and momentum?

In summary, the conversation revolved around the topic of the Schrödinger equation and its fundamental link between average position and momentum. The author expressed a lack of understanding about this connection and sought input from others on how to combine wave functions and the concept of superposition to better grasp the spreading of position through time. It was also noted that the author may benefit from studying classical analytical mechanics and quantum theory further before attempting to explain these concepts.
  • #1
AuxPart
1
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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 Schrodinger 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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  • #2
From the Schrödinger equation can be derived ...i wonder how to derive schrodinger 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 schrodinger equation.
 
  • #3
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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Likes drvrm
  • #4
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 vanhees71 and drvrm

1. What is the Schrödinger equation?

The Schrödinger equation is a mathematical equation that describes how the quantum state of a physical system changes over time. It is a fundamental equation in quantum mechanics and is used to predict the behavior of particles at the atomic and subatomic level.

2. How does the Schrödinger equation link position and momentum?

The Schrödinger equation includes two key operators: the position operator, which represents the position of a particle in space, and the momentum operator, which represents the momentum of a particle. The equation links these two operators through a mathematical relationship, allowing us to determine how the position and momentum of a particle change over time.

3. Why is the Schrödinger equation important?

The Schrödinger equation is important because it provides a way to describe and predict the behavior of particles at the quantum level. It has been used to successfully explain a wide range of phenomena, from the behavior of atoms and molecules to the properties of materials and the behavior of subatomic particles.

4. What does the Schrödinger equation tell us about particles?

The Schrödinger equation tells us about the probability of finding a particle in a certain position or with a certain momentum. It describes the behavior of particles at the quantum level, which is very different from the behavior of particles at the macroscopic level. It also allows us to make predictions about the behavior of particles and their interactions with other particles.

5. How is the Schrödinger equation derived?

The Schrödinger equation was first derived by Austrian physicist Erwin Schrödinger in 1926. He combined the classical equations for energy and momentum with the de Broglie hypothesis, which states that particles can exhibit wavelike behavior. This led to the development of the wave equation, which was later modified and became known as the Schrödinger equation.

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