Why the electron probability density is maximum at the nucleus? (split from Electron Probability distribution)

[Kartazion]

However, since I claim the uniqueness of the electron (even if there are several), it is logical that when there are several electrons therefore in an atom, to find a distribution which attenuates according to the distance from the nucleus. (because it is necessary to represent all the electrons with only one) and the more there is, the less its density presence becomes weak.

[swansont]

If electrons were unique they wouldn’t end up in all these different states. It’s because they are identical that they need to be in different n, l or m states to satisfy the Pauli exclusion principle  

[Kartazion]

With all due respect, it is precisely thanks to the Pauli exclusion principle that the electron cannot be in the same state. If the electron is on A or 1, it cannot be on A or 1 on another shell in the same time. In other words, if it is represented on the left, it cannot be on the left on its other orbital. As stated by John Wheeler, the electron is the same everywhere because its mass and its energy is the identical for all electrons.

[studiot]

35 minutes ago, Kartazion said:

the electron is the same everywhere because its mass and its energy is the identical for all electrons.

I very much doubt if Wheeler said exactly this.

For the very simple reason that  a free electron accelerated to 0.85c has quite a different energy from the electron still confined within the gun of the electron source, waiting to be freed and accelerated.

[Kartazion]

22 minutes ago, studiot said:

I very much doubt if Wheeler said exactly this.

Indeed he spoke of mass and charge. Energy was not the right term.

Quote

According to Feynman:

I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, "Feynman, I know why all electrons have the same charge and the same mass" "Why?" "Because, they are all the same electron!"

One-electron universe - Wikipedia
 

 

22 minutes ago, studiot said:

For the very simple reason that  a free electron accelerated to 0.85c has quite a different energy from the electron still confined within the gun of the electron source, waiting to be freed and accelerated.

Yes I was wrong. But:

Quote

In hydrogenoid atoms, the energy of an orbital is only a function of its main quantum number, n, which means that all the orbitals of the same shell will have the same energy. In a single-electron atom, an electron in a 2s orbital will have exactly the same energy as an electron in a 2p orbital, because they only interact with the nucleus through a Coulombic interaction

Edited June 19, 2021 by Kartazion
typo

[swansont]

1 hour ago, Kartazion said:

With all due respect, it is precisely thanks to the Pauli exclusion principle that the electron cannot be in the same state.

“all due respect” usually indicates disagreement. One of the components of the PEP is that you have identical particles, as I indicated. If they are unique they aren’t identical.

Quote

If the electron is on A or 1, it cannot be on A or 1 on another shell in the same time. In other words, if it is represented on the left, it cannot be on the left on its other orbital. As stated by John Wheeler, the electron is the same everywhere because its mass and its energy is the identical for all electrons.

If it’s on “another shell” then there is some difference in its state (whatever you mean by A or 1; we do have actual physics terminology we could use)

e.g. an electron in n=2 and the s state, can be spin up, and also have an electron in n=3, s state that is spin up. Such as you’d find in Ar.

“on the left” really has no meaning in this context.

[Kartazion]

4 minutes ago, swansont said:

“all due respect” usually indicates disagreement.

Yes seeing that I do not agree ..

4 minutes ago, swansont said:

If they are unique they aren’t identical.

I am unique. So not identical?

[swansont]

2 minutes ago, Kartazion said:

Yes seeing that I do not agree ..

And yet what you wrote is in agreement with what I wrote regarding the PEP

Quote

I am unique. So not identical?

No, there is nobody identical to you.

In hydrogenoid atoms, the energy of an orbital is only a function of its main quantum number, n, which means that all the orbitals of the same shell will have the same energy. In a single-electron atom, an electron in a 2s orbital will have exactly the same energy as an electron in a 2p orbital, because they only interact with the nucleus through a Coulombic interaction

Citation? You quote something, you need to provide a link. There’s probably something that says this is what’s predicted by the Schrödinger equation.

This turns out to not be true, once you delve a little deeper into quantum physics. It’s called the Lamb shift.

https://en.wikipedia.org/wiki/Lamb_shift

This also ignores the hyperfine splitting, where the spin of the electron matters in determining the energy.

[Kartazion]

I am unique (same size, same name). I am in Miami, I cannot be in Washington DC at the same time and vice versa. But in both cases I'm in the United States, but not in Europe. Yet we are all on earth.

It's a subtle and ambiguous question.

I now ask you the question: Why the electron probability density is maximum at the nucleus?

@swansont I just saw your answer to change or evolve. How is it that there is no "edit" stipulated?

[swansont]

2 hours ago, Kartazion said:

I am unique (same size, same name). I am in Miami, I cannot be in Washington DC at the same time and vice versa. But in both cases I'm in the United States, but not in Europe. Yet we are all on earth.

It's a subtle and ambiguous question.

Not really. You are not a quantum particle, and location isn’t a property that has a quantum number.

Can we deal with actual QM and not analogies? That removes much of the ambiguity.

2 hours ago, Kartazion said:

I now ask you the question: Why the electron probability density is maximum at the nucleus?

Answered. It’s because of the math, both “this is what the math is” and “because you’re using spherical coordinates”; the volume element depends on the radius. The probability density isn’t the quantity with physical meaning, so there isn’t a physical justification I can give.

 

2 hours ago, Kartazion said:

@swansont I just saw your answer to change or evolve. How is it that there is no "edit" stipulated?

Answers get merged. And if I edit immediately, I usually don’t annotate it.

[Kartazion]

13 minutes ago, swansont said:

Not really. You are not a quantum particle, and location isn’t a property that has a quantum number.

Can we deal with actual QM and not analogies? That removes much of the ambiguity.

What material are we made of then?
 

14 minutes ago, swansont said:

Answered. It’s because of the math, both “this is what the math is” and “because you’re using spherical coordinates”; the volume element depends on the radius. The probability density isn’t the quantity with physical meaning, so there isn’t a physical justification I can give.

Ok

Thanks

I think I can give an explanation with my unique particle principle to explain a decrease when multiplying the number of electrons. But my question then turns to a Ridberg atom of hydrogen. Is the excited electron subject to this decrease in probability density when it is on a high n shell?

PS:

40 minutes ago, swansont said:

... and location isn’t a property that has a quantum number.

You first told me about the Pauli exclusion principle.

As you know (we know each other quite well) I am a novice and not confirmed in the discipline of the QM. But I think that analogies are a good tool to be able to best explain certain mechanisms or principles. This makes it possible to have a more understandable approach or thought experience of the subject in question.

I know and I think that your task as moderators should not be obvious, especially since I am quite and for my part, persisting in my objective.

However, the goal of my talk is to be able to respond to quantum strangeness in a unifying formula.

The unification of the principle of the single particle concerns and of course:

- Galaxy
- Supermassive black hole
- Hawking Radiation
- Dark matter
- Star
- Planet
- Quantum entanglement
- Quantum superposition
- Quantum Vacuum and Vacuum Energy
- Quantum chromodynamics
- Quark
- Gluon
- Neutrino
- Antimatter
- CPT symmetry
- Supersymmetry
- Schrödinger's paradox
- Heisenberg Uncertainty Principle
- Time dilation
- Dark Energy

- Gravity
- Tunnel effect

- Electromagnetic wave
- Weak interaction
- Electron

Remember. I start with this topic:

https://www.scienceforums.net/topic/116040-hologram-with-only-one-particle-in-motion/

Then I associated the single particle principle with an anharmonic oscillator where the particle oscillates between singularity and matter:

https://www.scienceforums.net/topic/120416-anharmonic-oscillator/

 

[swansont]

8 hours ago, Kartazion said:

What material are we made of then?
 

I don’t see how that’s relevant to the topic.

8 hours ago, Kartazion said:

 

I think I can give an explanation with my unique particle principle to explain a decrease when multiplying the number of electrons. But my question then turns to a Ridberg atom of hydrogen. Is the excited electron subject to this decrease in probability density when it is on a high n shell?

You can look at the graph (or equation) of the probability density for various n levels and compare.

 

8 hours ago, Kartazion said:

PS:

You first told me about the Pauli exclusion principle.

If you have questions about it you should ask.

8 hours ago, Kartazion said:

As you know (we know each other quite well) I am a novice and not confirmed in the discipline of the QM. But I think that analogies are a good tool to be able to best explain certain mechanisms or principles. This makes it possible to have a more understandable approach or thought experience of the subject in question.

You perhaps overestimate how much I keep track of others’ backgrounds.

If you want to discuss QM, and especially if you assert that it works a certain way, I assume a certain level of familiarity. If that’s lacking, then this is a waste of time; you can’t build a proper model or assess criticism of your idea.

8 hours ago, Kartazion said:

I know and I think that your task as moderators should not be obvious, especially since I am quite and for my part, persisting in my objective.

However, the goal of my talk is to be able to respond to quantum strangeness in a unifying formula.

The unification of the principle of the single particle concerns and of course:

- Galaxy
- Supermassive black hole
- Hawking Radiation
- Dark matter
- Star
- Planet
- Quantum entanglement
- Quantum superposition
- Quantum Vacuum and Vacuum Energy
- Quantum chromodynamics
- Quark
- Gluon
- Neutrino
- Antimatter
- CPT symmetry
- Supersymmetry
- Schrödinger's paradox
- Heisenberg Uncertainty Principle
- Time dilation
- Dark Energy

- Gravity
- Tunnel effect

- Electromagnetic wave
- Weak interaction
- Electron

The topic here is the electron’s wave function and probability density.

8 hours ago, Kartazion said:

Remember. I start with this topic:

https://www.scienceforums.net/topic/116040-hologram-with-only-one-particle-in-motion/

Then I associated the single particle principle with an anharmonic oscillator where the particle oscillates between singularity and matter:

https://www.scienceforums.net/topic/120416-anharmonic-oscillator/

 

Tying in to other speculative ideas is against the rules. 

[Kartazion]

2 hours ago, swansont said:

I don’t see how that’s relevant to the topic.

I'll teach you something. We are made of quantum particles. Believe it or not. That why.
 

2 hours ago, swansont said:

You can look at the graph (or equation) of the probability density for various n levels and compare.

Indeed the graphic result confirms my position.
 

2 hours ago, swansont said:

If you have questions about it you should ask.

I have no questions on this principle. But you told me about it.
 

2 hours ago, swansont said:

You perhaps overestimate how much I keep track of others’ backgrounds.

After three years of discussion between the two of us (yes it is only often the two of us) don't you remember me?
 

2 hours ago, swansont said:

If you want to discuss QM, and especially if you assert that it works a certain way, I assume a certain level of familiarity. If that’s lacking, then this is a waste of time; you can’t build a proper model or assess criticism of your idea.

Do you? Or are you just following what you've learned? Maybe you save time learning to others.
 

2 hours ago, swansont said:

The topic here is the electron’s wave function and probability density.

I thought also. But the principle of the single particle concerns the electron’s wave function and probability density.
 

2 hours ago, swansont said:

Tying in to other speculative ideas is against the rules. 

I did not know that the description and speculative links of this forum break the rules of the speculation section of this forum.

[studiot]

13 minutes ago, Kartazion said:

Indeed the graphic result confirms my position.

What I find confusing is that I can't see what 'your position' is.

I understand that most authors skate quickly over some part of the derivation and also use different terminology that need to be sorted out.

For instance your graph from the Khan academy is not a graph of probability density. Nor is it a graph of the quantities shown in arnav's parent thread.

It is, and says it is, a graph of probability.

 

In order to understand how your question is handled, it is necessary to be able to distinguish between eigenvalues and eigenfunctions of differential equations as both of these are involved in the principal and subsidiary quantum numbers n, m and l.

A knowledge of symmetry, improper integrals would also help.

But this is also a case of alternating the Physics and the Maths in the derivation.

Authors introduce two different mathematical devices to handle the improper integrals, one is called the Probability Density the other is called the Probability Flux or Probability Current.

 

To understand what is going on you need to start with the physics of the field of the nucleus.
Do you know how to do this ?

[swansont]

24 minutes ago, Kartazion said:

I'll teach you something. We are made of quantum particles. Believe it or not. That why.

 

And? 

You need to include the part where you explain how this has relevance 

 

24 minutes ago, Kartazion said:

Indeed the graphic result confirms my position.

 

Not clear what your position is.

24 minutes ago, Kartazion said:

I have no questions on this principle. But you told me about it.

So this, too, is irrelevant to the topic.

24 minutes ago, Kartazion said:

After three years of discussion between the two of us (yes it is only often the two of us) don't you remember me?

That’s not what I said, so I don’t know what prompts this question. Reading comprehension issues?

 

24 minutes ago, Kartazion said:

I did not know that the description and speculative links of this forum break the rules of the speculation section of this forum.

Rule 2.5 Stay on topic. Posts should be relevant to the discussion at hand. This means that you shouldn't use scientific threads to advertise your own personal theory, or post only to incite a hostile argument.

 

[Kartazion]

29 minutes ago, studiot said:

What I find confusing is that I can't see what 'your position' is.

24 minutes ago, swansont said:

Not clear what your position is.

Are you kidding me? My position is to claim the creation of the universe with a single moving particle.
 

30 minutes ago, studiot said:

For instance your graph from the Khan academy is not a graph of probability density. Nor is it a graph of the quantities shown in arnav's parent thread.

Do you prefer the hyperphysics.phy-astr.gsu.edu graph?
http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html

 

32 minutes ago, studiot said:

To understand what is going on you need to start with the physics of the field of the nucleus.
Do you know how to do this ?

The physics of the field of the nucleus to understand the density distribution of the electron? Can you enlighten me on this subject? This surely has an electric charge ratio. Thank you.
 

28 minutes ago, swansont said:

And? 

You need to include the part where you explain how this has relevance

It is because you said that I am not a quantum particle. I simply replied that we are made of quantiuqe particles.
 

29 minutes ago, swansont said:

Rule 2.5 Stay on topic. Posts should be relevant to the discussion at hand. This means that you shouldn't use scientific threads to advertise your own personal theory, or post only to incite a hostile argument.

So I just have one thing to say. John Wheeler is a theoretical physicist who speculates.

[studiot]

2 minutes ago, Kartazion said:

Do you prefer the hyperphysics.phy-astr.gsu.edu graph?
http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html

Nor is this a graph of probability density.

And it says basically the same as your Khan graph.

Both are the result of several pages of working in Maths and Physics.

4 minutes ago, Kartazion said:

The physics of the field of the nucleus to understand the density distribution of the electron?

What is the density distribution of the electron ?

 

I have already warned against confusing Probability with Probability Density, they are not the same.

Look at the post I just made in Arnav's thread before you answer.

[Kartazion]

5 minutes ago, studiot said:

What is the density distribution of the electron ?

7 minutes ago, studiot said:

I have already warned against confusing Probability with Probability Density, they are not the same.

I did not understand...

 

10 minutes ago, studiot said:

Look at the post I just made in Arnav's thread before you answer.

Ok. But I do not see

...

Ah ok I saw for the nucleus ...

[studiot]

27 minutes ago, Kartazion said:

 

 

Which, to quote swansont's comment, is irrelevant.

This is about the density of many electrons in materials (look it says so) It for for consideration of metals, semiconductors etc.

We are discussing one electron within a single atom.

 

I do accept that there are many similar sounding terms so we should all be careful not to mix them up.
It is very easy to fall into this trap.

Edited June 20, 2021 by studiot

[swansont]

1 hour ago, Kartazion said:

It is because you said that I am not a quantum particle. I simply replied that we are made of quantiuqe particles.

Meanwhile you are still not a quantum particle. The physics of your behavior is quite adequately described by classical physics, and this is still not relevant to the topic of the thread.

[Kartazion]

1 hour ago, swansont said:

Meanwhile you are still not a quantum particle. The physics of your behavior is quite adequately described by classical physics, and this is still not relevant to the topic of the thread.

This was relevant to be able to make a good analogy. On the other hand, you have rejected my analogy to the detriment of the real behavior of the quantum particle.
 

I recall that this analogy focused on the Pauli exclusion principle.

[swansont]

1 hour ago, Kartazion said:

This was relevant to be able to make a good analogy. On the other hand, you have rejected my analogy to the detriment of the real behavior of the quantum particle.

A behavior you have admitted to not studying and having no expertise in understanding.

Analogies are limited in usefulness. Analogies of quantum systems are typically more limited. Again, it’s preferable to actually discuss QM.

[Kartazion]

Hello.
 

18 hours ago, swansont said:

Analogies are limited in usefulness. Analogies of quantum systems are typically more limited. Again, it’s preferable to actually discuss QM.

Alright. I'm working on it.

 

23 hours ago, studiot said:

For instance your graph from the Khan academy is not a graph of probability density. Nor is it a graph of the quantities shown in arnav's parent thread.

23 hours ago, Kartazion said:

Do you prefer the hyperphysics.phy-astr.gsu.edu graph?
http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html
 

23 hours ago, studiot said:

Nor is this a graph of probability density.

 

For the electron in the atom, can you please give me an example of a probability density graph?

Thanks.

[Kartazion]

Here is a probability plot of electron density in a heavy atom:

Ψ2 gives the probability of finding an electron in a given volume of space.
The distance from the nucleus (r) gives the probability density.
 

 

But if we were to add the mass of electrons in relation to their real numbers, then the electron mass density would look like this:
 

What is the mass density distribution of an electron?
 

Quote

Fundamental properties

The invariant mass of an electron is approximately 9.109×10−31 kilograms, or 5.489×10−4 atomic mass units. On the basis of Einstein's principle of mass–energy equivalence, this mass corresponds to a rest energy of 0.511 MeV. 

https://en.wikipedia.org/wiki/Electron#Fundamental_properties

 

Edited June 22, 2021 by Kartazion

[Kartazion]

On 6/20/2021 at 1:59 PM, studiot said:

This is about the density of many electrons in materials (look it says so) It for for consideration of metals, semiconductors etc.

But why ask me when I'm showing the real?
 

On 6/20/2021 at 1:26 PM, studiot said:

What is the density distribution of the electron ?

The electron density distribution is the same from the start.



 

On 6/19/2021 at 7:55 PM, Kartazion said:

 

On 6/20/2021 at 12:41 PM, studiot said:

For instance your graph from the Khan academy is not a graph of probability density. Nor is it a graph of the quantities shown in arnav's parent thread.

 

Not a graph of probability density?

Can you expand?

Thanks