Anharmonic Oscillator

[Kartazion]

On 2/21/2020 at 10:52 PM, swansont said:

Without existing in between those points? 

As you can see, the particle disappears when it moves too fast. And appears on its extremities because it marks a certain stop.
It is an optical illusion known as Optical flow. And that is calculated. Why not have done the approximation?

Reminder:
When you increase the speed to 20 or 40, you will achieve perfect harmony. --> See the animation

So we can see two distinct dots from a single particle. 

Edited April 5, 2020 by Kartazion

[Strange]

1 hour ago, Kartazion said:

As you can see, the particle disappears when it moves too fast.

It only disappears because the display cannot render the intermediate positions (or, if it were a physical object) because the eye cannot react that fast. 

You are playing around with optical illusions. This has nothing to do with quantum theory. I'm not sure why this thread has been allowed to drag on for so long.

[Kartazion]

1 minute ago, Strange said:

It only disappears because the display cannot

the intermediate positions (or, if it were a physical object) because the eye cannot react that fast. 

Yes.

8 minutes ago, Strange said:

You are playing around with optical illusions.

And as said before this is calculated.

13 minutes ago, Strange said:

This has nothing to do with quantum theory. I'm not sure why this thread has been allowed to drag on for so long.

I am only emphasizing the result of the very high frequency anharmonic oscillation.
In addition this thread talk about of a classical and not quantum oscillator.

[Strange]

13 minutes ago, Kartazion said:

I am only emphasizing the result of the very high frequency anharmonic oscillation.

No you are not. You said, "As you can see, the particle disappears when it moves too fast" which is not true. It does not disappear.

So you are lying being deliberately inaccurate about "the result of the very high frequency anharmonic oscillation."

13 minutes ago, Kartazion said:

In addition this thread talk about of a classical and not quantum oscillator.

Also not true. There are about 30 posts where you have mentioned quantum theory. And you were the first to introduce the topic.

[Kartazion]

8 minutes ago, Strange said:

No you are not. You said, "As you can see, the particle disappears when it moves too fast" which is not true. It does not disappear.

So you are lying about "the result of the very high frequency anharmonic oscillation."

Yes its probability of presence allows it. Because the anharmonicity is focused on the stop of the particle at its ends, unlike, where between two, its acceleration is very fast.
You are therefore more likely to find the particle at its ends, than between.

[Kartazion]

13 hours ago, Strange said:

Also not true. There are about 30 posts where you have mentioned quantum theory. And you were the first to introduce the topic.

I had not seen the addition and modification of your message.

I misspoke. I should have clarified again that I was based on the arrangement of this subject which has been clarified since.

On 2/21/2020 at 12:06 AM, Kartazion said:

Split reference:

 

Conclusion: The oscillator that I am trying to exploit is classical and not quantum.
 

 

[Strange]

1 minute ago, Kartazion said:

Conclusion: The oscillator that I am trying to exploit is classical and not quantum.

So you are no longer claiming that this is some sort of explanation or model of quantum effects? If so, good. That is some sort of progress.

[Kartazion]

40 minutes ago, Strange said:

So you are no longer claiming that this is some sort of explanation or model of quantum effects? 

I'm not savvy enough to be able to say it. Maybe the same electron is oscillating with another electron.

But my oscillator is classic.

[Kartazion]

Strange, do you agree with that: 

You are therefore more likely to find the particle at its ends, than between. Because the anharmonicity is focused on the stop of the particle at its ends, unlike, where between two, its acceleration is very fast.

[Kartazion]

Can we associate a wave function with a classical oscillator system?

[swansont]

26 minutes ago, Kartazion said:

Can we associate a wave function with a classical oscillator system?

Yes. Why would you want to?

[Kartazion]

7 minutes ago, swansont said:

Yes. Why would you want to?

To show the probability of the presence of the particle.

[swansont]

2 hours ago, Kartazion said:

To show the probability of the presence of the particle.

It becomes the classical solution when n is large. Again: why would you want to do this?

[Kartazion]

1 hour ago, swansont said:

Again: why would you want to do this?

I wanted, with the wave function, to exploit the classical presence form of the particle as the electron in a hydrogen atom at different energy levels such as 4,3,3

I remind you that I'm a novice and I haven't figured it all out yet. So I think I'm going in the wrong direction to explain this, with a classical particle ; or not.

[swansont]

35 minutes ago, Kartazion said:

I wanted, with the wave function, to exploit the classical presence form of the particle as the electron in a hydrogen atom at different energy levels such as 4,3,3

I remind you that I'm a novice and I haven't figured it all out yet. So I think I'm going in the wrong direction to explain this, with a classical particle ; or not.

n=4 isn't going to give you a classical solution. n = 4000 might.These systems are hard to investigate because they are so easy to ionize at that point.

[studiot]

2 hours ago, Kartazion said:

I wanted, with the wave function, to exploit the classical presence form of the particle as the electron in a hydrogen atom at different energy levels such as 4,3,3

 

I remind you that I'm a novice and I haven't figured it all out yet. So I think I'm going in the wrong direction to explain this, with a classical particle ; or not.

 

I know you haven't followed up any of the references I have already given but you might like to look at this one.

Chapter 2 of

Molecular Quantum Mechanics by Atkins and Friedman is largely about your current discussion with swansont.

In particular they work out in great detail the difference between the classical harmonic oscillator and a quantum (probability) one with many plots and diagrams similar to the ones you are looking at. It would save you a lot of work and offers a great deal of explanation about what is and is not possible.

[Kartazion]

9 hours ago, studiot said:

I know you haven't followed up any of the references I have already given but you might like to look at this one.

I've only been in the study phase for a few weeks. It is difficult for me to follow everything as mathematical evidence.
What is the reference that I should have followed in order to be able to talk about the probability of presence of the particle?

9 hours ago, studiot said:

Chapter 2 of

Molecular Quantum Mechanics by Atkins and Friedman is largely about your current discussion with swansont.

Thanks for the tip. It's a great document as a whole, but it's highly quantum.

[Kartazion]

On 4/29/2020 at 7:56 PM, swansont said:

n=4 isn't going to give you a classical solution. n = 4000 might.These systems are hard to investigate because they are so easy to ionize at that point.

Isn't that the Rydberg atom principle? With a high n value? 

[swansont]

39 minutes ago, Kartazion said:

Isn't that the Rydberg atom principle? With a high n value? 

Yes, that would be a Rydberg state. Which approaches a classical solution.

[Kartazion]

44 minutes ago, swansont said:

Yes, that would be a Rydberg state. Which approaches a classical solution.

For fun; one could create an oscillator of the electron of a hydrogen atom with the variation of the wavelength of a laser assimilated to the electronic layers. 
This variation could be done between the false vacuum (surely the ground state) and the highest excited state of the potential well. Without ionization of course. 
As an output we could then study the Rydberg wave packet.

The question is, why, or in what sense would this be a classic solution approach when we have a big n?

Thanks.

[studiot]

On 4/30/2020 at 6:04 AM, Kartazion said:

Thanks for the tip. It's a great document as a whole, but it's highly quantum.

Which is hardly surprising considering the title.

1 hour ago, Kartazion said:

The question is, why, or in what sense would this be a classic solution approach when we have a big n?

Nevertheless if you had read the reference it would have explained this with diagrams you could follow.

[swansont]

4 hours ago, Kartazion said:

For fun; one could create an oscillator of the electron of a hydrogen atom with the variation of the wavelength of a laser assimilated to the electronic layers. 

Not sure what this means.

4 hours ago, Kartazion said:

This variation could be done between the false vacuum (surely the ground state)

False vacuum? An atom isn’t a vacuum. and a false vacuum implies a lower energy state. What state is below the ground state?

4 hours ago, Kartazion said:

and the highest excited state of the potential well. Without ionization of course. 

n goes to infinity, so there is no highest state.

 

4 hours ago, Kartazion said:

The question is, why, or in what sense would this be a classic solution approach when we have a big n?

Thanks.

The energy state differences become small, approximating a continuum. The orbital angular momentum changes, too, and approaches the classical solution for large L

[Kartazion]

11 minutes ago, swansont said:

What state is below the ground state?

The true vacuum?

12 minutes ago, swansont said:

False vacuum? An atom isn’t a vacuum. and a false vacuum implies a lower energy state. 

n goes to infinity, so there is no highest state.

But the energy and thus the principal quantum number n follow the shape of the potential well?

https://www.academia.edu/8950511/Molecular_Quantum_Mechanics_4th_ed_ATKINS-FRIEDMAN

[swansont]

56 minutes ago, Kartazion said:

The true vacuum?

How does that apply to an atom?

56 minutes ago, Kartazion said:

But the energy and thus the principal quantum number n follow the shape of the potential well?

n follows the shape of the potential well? What does that mean?

Energy depends on n, but they are not the same thing. In hydrogen, for example, it depends on 1/n^2

 

56 minutes ago, Kartazion said:

https://www.academia.edu/8950511/Molecular_Quantum_Mechanics_4th_ed_ATKINS-FRIEDMAN

That’s the probability distribution, not the energy

[Kartazion]

55 minutes ago, swansont said:

How does that apply to an atom?

For the atomic nucleus I don't know. But the electron can use quantum tunnelling and pass the potential barrier from the false to the true vacuum.
In the QFT the Higgs potential determines whether the Universe is in one of a true vacuum, or a false vacuum.

1 hour ago, swansont said:

n follows the shape of the potential well? What does that mean?

Doesn't the ground state represent the lowest energy level of an atom? And so at the bottom of the well at x=0?
So that a large value of n could bring the energy to the highest in the well?

1 hour ago, swansont said:

Energy depends on n, but they are not the same thing. In hydrogen, for example, it depends on 1/n^2

Ok.

1 hour ago, swansont said:

That’s the probability distribution, not the energy

We have a better chance of finding the particle at the extremities than in the center of the well.