Ground State Energy: What Regulates & Why is it Constant?

[nuby]

What regulates the ground state energy of a hydrogen atom? Why is it constant (more or less)?

 

[Marco_84]

check perturbation theories ;)

 

[saray1360]

hi,

as far as I know there are theoretical relations by which you calculate the ground state of a system. Like Kohn-Sham equation and ...
The density functional theory texts may help you. The atomic systems usually converge to a ground state energy which is unique, but theoretically very hard to calculate...

Hope it helped.

Good luck!

 

[nuby]

Thanks for the post. I was mostly wondering which force regulates the ground state, and if it is related to the Lorentz force.

 

[jtbell]

The ground state energy of hydrogen comes from the solution of Schrödinger's equation for the Coulomb (electric) potential energy function of the electron and proton.

 

[ZapperZ]

What regulates the ground state energy of a hydrogen atom? Why is it constant (more or less)?

What exactly do you mean by "regulate"?

Zz.

 

[nuby]

What exactly do you mean by "regulate"?

Zz.

"Holds" the binding force (potential?) at around -27.2 eV , and electron kinetic energy at +13.6 eV.

 

[ZapperZ]

"Holds" the binding force (potential) at around -27.2 eV , and electron kinetic energy at +13.6 eV.

Binding force potential? Kinetic energy?

Even in the simplest Rydberg atom model, is it not obvious that we have a Coulombic potential? I mean, you have a positive nucleus, and a negative electron. Is there something here that I'm missing?

Zz.

 

[nuby]

Binding force potential? Kinetic energy?

Even in the simplest Rydberg atom model, is it not obvious that we have a Coulombic potential? I mean, you have a positive nucleus, and a negative electron. Is there something here that I'm missing?

Zz.

That works too, the Coulombic potential of ground state. What controls it?

 

[ZapperZ]

That works too, the Coulombic potential of ground state. How is it determined?

Er... this is classical E&M. If you have a spherically symmetry + charge at the origin, what is the electrostatic potential at point r?

Zz.

 

[nuby]

I meant "what controls it" .. I edited my post right after you responded.

 

[ZapperZ]

I meant "what controls it" .. I edited my post right after you responded.

Control?

This is meant to clarify?

What's the issue that you have with electrostatic potential?

Zz.

 

[edguy99]

"Holds" the binding force (potential?) at around -27.2 eV , and electron kinetic energy at +13.6 eV.

I am guessing you mean that why does the electron not gain more then 13.6 ev of kinetic energy as it falls closer to the proton?

On the lower end, I don't think that the electron needs to keep at least 13.6 ev of kinetic energy, the electrons kinetic energy can be much lower and I think usually would be. Hydrogen gas with electrons buzzing around with 13.6 ev of energy would be considered very "hot".

 

[nuby]

these might make more sense.

1.) Why does the electron energy remain constant in ground state hydrogen, as well as the average size of the atom?

2.) Why don't protons and anti-protons interact like protons and electrons?

Thanks in advance

 

[ZapperZ]

these might make more sense.

1.) Why does the electron energy remain constant in ground state hydrogen, as well as the average size of the atom?

Because when you set it up quantum mechanically, you get solutions to the Hamiltonian that corresponds to the "stationary" solutions that you get when you solve the classical Hamiltonian. Based on the physics that we know, this is the definition of the ground state.

2.) Why don't protons and anti-protons interact like protons and electrons?

Thanks in advance

Because a proton is a baryon and an electron is a lepton, where is a proton/anti-proton are both baryon and the physics indicates that they are "mirror image" of each other, separated only by a few symmetry operations. You can't do the same with proton and electrons, which are both matter and not even identical to each other in many respects.

Have you looked at basic physics text (or even the internet) to actually do your own legwork on the obvious difference between these two sets of conditions that you have asked? I mean, I'm sure you would have realized that proton-antiproton are more alike to each other than proton-electron. They do at least teach such a thing in high school, don't they, regarding the "scale" of things, such as the different in mass between proton and electron?

Zz.

 

[nuby]

Because a proton is a baryon and an electron is a lepton, where is a proton/anti-proton are both baryon and the physics indicates that they are "mirror image" of each other, separated only by a few symmetry operations. You can't do the same with proton and electrons, which are both matter and not even identical to each other in many respects.
Zz.

So the forces between the two leptons (electrons / positrons) behave a lot differently, than between leptons and baryons.

 

[ZapperZ]

You notice that you have changed topic.

I still want to know why you are having problems with a simple, straight-forward electrostatic potential.

Zz.

 

[nuby]

I guess I'm wondering if the ground state electrostatic potential (or electron) interacts with the zero-point-field, and if the ZPF dictates the ground state energy?

 

[granpa]

I doubt it.

the reason the electron can't fall into the proton is that it is too big. a proton and an antiproton are the same size so they can cancel each other out completely. a proton and an electron can't do that.

how big the electron is depends on how you define it. I prefer to think of the size of the electron as the size of its charge cloud.

 

[nuby]

I doubt it.

the reason the electron can't fall into the proton is that it is too big. a proton and an antiproton are the same size so they can cancel each other out completely. a proton and an electron can't do that.

This seems strange. Are you saying a proton can't fall into an electron because they don't have the same mass-energy, or volume?

 

[granpa]

there is nothing in my post about a proton falling into a proton which would be strange indedd since they would electrostatically repel one another.

all I said was that the electron is (much) bigger than a proton.

 

[nuby]

there is nothing in my post about a proton falling into a proton which would be strange indedd since they would electrostatically repel one another.

all I said was that the electron is (much) bigger than a proton.

I meant proton / electron. I'm still not clear on what your are saying. Are you saying the electron is so small it passes through the proton, which is why they don't 'crash' into each other?

 

[granpa]

read post 21 again

 

[nuby]

"the reason the electron can't fall into the proton is that it is too big." What is this supposed to mean?

 

[granpa]

it means that it (the electron) is too big

 

[granpa]

of course, the electron does fall into the proton during electron capture. the result is a neutron. but neutrons are unstable. they spontaneously break back down into protons and electrons (beta decay) with a considerably release of energy.

you might find this interesting.
http://physics.nist.gov/GenInt/Parity/expt.html

 

[ZapperZ]

it means that it (the electron) is too big

Can you please go to the Particle Data Book and show me where an electron is "much bigger" than a proton?

Zz.

 

[granpa]

can you please read post 19.

 

[ZapperZ]

can you please read post 19.

I did! That is why I asked you to look up in the Particle Data Book and (i) find out what is meant by the SIZE of an electron and (ii) why it is significantly larger than a proton.

According to your definition, if I throw a tennis ball around a tennis court, the SIZE of the tennis ball is as large as the tennis court itself. Does this make any sense to you? And more importantly, is this ACCURATE?

Zz.

 

[Vanadium 50]

can you please read post 19.

how big the electron is depends on how you define it. I prefer to think of the size of the electron as the size of its charge cloud.

Proof by preference?

ZapperZ is exactly right with his tennis court analogy.

 

[snapback]

an interesting approach to the problem of hydrogen ground state can be found here:

http://arxiv.org/abs/quant-ph/0307154"

cheers


oops, sorry, have not seen that nuby already mentioned ZPF.. but that paper might be related to his post 18

 

[JeffKoch]

"Holds" the binding force (potential?) at around -27.2 eV , and electron kinetic energy at +13.6 eV.

If you're referring to the particular numbers, they're in arbitrary units but 13.6 comes from the rest mass of the electron in eV and the fine structure constant. So the question really boils down to why the dimensionless fine-structure constant is what it is, and I don't think anyone has an answer to that question.

 

[Modey3]

nuby,

1.) Why does the electron energy remain constant in ground state hydrogen, as well as the average size of the atom?

You don't need to go into particle physics to answer this question! You have a coulombic potential between the electron and proton. This is a quantum mechanical system! If you solve the Hamiltonian for this system you get a set of eigenvalues which correspond to stationary energies. Stationary energies are energies which correspond to a minimum in the 3-dimensional energy surface. For the hydrogen atom there are 3 quantum numbers: n, l, ml which describe the wave function for the system. I am disregarding the spin quantum number since the electron spin isn't effect by the Hamiltonian. The restriction is that these quantum numbers must be integers. These integers correspond to stationary solutions. If by some perturbation that n went from n = 2 to n = 2.1. The electron would spontaneously go back to n = 2 because that is a stationary state - it's at the bottom of the hill.

modey3

 

[nuby]

How does the zero-point field come into the equation?

 

[snapback]

Random oriented zero-point field overpowers the directed (along the line between electron and proton) attraction between proton and electron at short distances and makes, sloppy speaking, the electron "lose its way on its fall towards proton"

To my knowledge ZPF is not included explicitly in the Hamiltonian approach where you rely (by assumption) on the fact that a hermitian operator has a lower bound in its spectrum. By "explicitly" I mean: ... well ... you can always discuss what the physics behind the existence of a lower bound of a hermitian operator is.

What about positronium, why does that thing annihilate ? Here the interaction between the components is also coulombic, at least at large distances.

 

[Redbelly98]

How does the zero-point field come into the equation?

That's a rather complicated calculation. There are even people with Ph.D.'s in physics who do not know how to do it.

The effect is quite small, though. For the n=2 level of hydrogen it's a few micro eV.

 

[snapback]

That's a rather complicated calculation. There are even people with Ph.D.'s in physics who do not know how to do it.

The effect is quite small, though. For the n=2 level of hydrogen it's a few micro eV.

I bet you are referring to Lamb-shift (fine structure of the n=2 level) ?
Please note, Lamb-shift affects the n=2 level, the discussion here is about the ground state (n=1).

What regulates the ground state energy of a hydrogen atom? Why is it constant (more or less)?

 

[Redbelly98]

I bet you are referring to Lamb-shift (fine structure of the n=2 level) ?
Please note, Lamb-shift affects the n=2 level, the discussion here is about the ground state (n=1).

Please note, I did explicitly say n=2 in my post. Also, discussions often shift or expand in scope by the time you get to the 30th post in a thread.

I wanted to make the point that the effect of vacuum fluctuations:

• Is not a simple matter to calculate.
• Is small compared to the overall hydrogen energy. I don't know the value for the ground state, so I quoted the amount of the Lamb shift for n=2*** to give a sense of it's small contribution to the overall energy

If you happen to know how much the ground state is affected by vacuum fluctuations, or a simple way to estimate it, I would be interested in knowing that.

Regards,

Mark

*** EDIT: 1057 MHz or 4.371 x 10^-6 eV

 

[snapback]

Please note, I did explicitly say n=2 in my post. Also, discussions often shift or expand in scope by the time you get to the 30th post in a thread.

I simply wanted to stay within the ground-state topic (well, it might be a little stubborn after 30th post ;-))

Sadly, I cannot help you with any estimation how much the ground state is affected by vacuum fluctuations. I'm aware of a http://arxiv.org/abs/quant-ph/0307154v1" , where it has been attempted to track the "behavior of a classical charged point particle under the influence of only a Coulombic binding potential and classical electromagnetic zero-point radiation" numerically. This calculation was done within the framework of classical stochastic electrodynamics (SED). No energy values are visible in this paper. And ... "55 days of CPU time for all runs" does not sound like a handy estimation ;-)

Nevertheless, don't you think it would be somehow amazing if vacuum fluctuations would be responsible for both effects: the energetically tiny Lamb shift at n=2 and the prevention of catastrophic collapse at n=1 ?

Regards

snapback

 

[Redbelly98]

Nevertheless, don't you think it would be somehow amazing if vacuum fluctuations would be responsible for both effects: the energetically tiny Lamb shift at n=2 and the prevention of catastrophic collapse at n=1 ?

Regards

snapback

Absolutely. I never meant to imply otherwise. My main point, that it is a small effect, addresses this earlier post (not the same one I quoted in Post #36):

I guess I'm wondering if the ground state electrostatic potential (or electron) interacts with the zero-point-field, and if the ZPF dictates the ground state energy?

A more direct answer would be: No. ZPF, also known as vacuum fluctuations, cause a small perturbation to the energy of the hydrogen atom.

 

[snapback]

If ZPF is not resonsible for the stability of the ground state, then we would need another force than electromagnetic force to oppose the steady attraction between electron and proton. As I see it: with electromagnetics gone, the number of suitable forces for prevention of the Hydrogen collapse is dramatically reduced (at least in the framework of standard model).

 

[Redbelly98]

If ZPF is not resonsible for the stability of the ground state, then we would need another force than electromagnetic force to oppose the steady attraction between electron and proton. As I see it: with electromagnetics gone, the number of suitable forces for prevention of the Hydrogen collapse is dramatically reduced (at least in the framework of standard model).

But, who says another force is required to prevent collapse? It's basic quantum mechanics that only discrete states are possible. electrostatic + kinetic energy are enough to explain what happens. Everything else--ZPF, gravity, and even magnetic interactions--are minor perturbations.

 

[snapback]

basic QM allows the calculation of measurement results (=discrete states) out of some postulates but gives no physical explanation why discrete states or the ground state exist. QM is a (very useful) calculational tool but it gives us no hints why Hydrogen is stable. But of course, if one supports the Copenhagen interpretation, then the results of QM calculations cannot be further scrutinized.

 

[Marco_84]

Having hamiltonian operators bounded from below
(i.e. we can have stables ground states) it isn't a quantum mechanical necessity.
It is an assumption already made during the XIX century.
It just states that the world we observe isn't collapsing on his-self.

I hope i was clear.

Marco

 

[snapback]

Having hamiltonian operators bounded from below
(i.e. we can have stables ground states) it isn't a quantum mechanical necessity.
It is an assumption already made during the XIX century.
It just states that the world we observe isn't collapsing on his-self.

I hope i was clear.

Marco

I regret, that your point is not clear to me. As I see it: there should be a physical mechanism behind any assumption.

 

[Marco_84]

I regret, that your point is not clear to me. As I see it: there should be a physical mechanism behind any assumption.

In fact, i wrote:

It is an assumption already made during the XIX century.
It just states that the world we observe isn't collapsing on his-self.

"This is the physical mechanism behind".

marco

 

[snapback]

I understand that there might be as many meanings of what a "physical mechanism"is, as there are physicists walking on the earth, so maybe I'm still missing your point.

In fact, i wrote:

It is an assumption already made during the XIX century.
It just states that the world we observe isn't collapsing on his-self.

"This is the physical mechanism behind".

marco

But what was in the 18th century, before that "assumption" was made ? Was there a "different" physical mechanism that prevented collapse ?

To me, the stability of Hydrogen is not merely an "assumption" but rather an empirical fact.

 

[Marco_84]

basic QM allows the calculation of measurement results (=discrete states) out of some postulates but gives no physical explanation why discrete states or the ground state exist. QM is a (very useful) calculational tool but it gives us no hints why Hydrogen is stable. But of course, if one supports the Copenhagen interpretation, then the results of QM calculations cannot be further scrutinized.

I'm sorry but my english is not so good :D.

What I'm trying to say is more general than just talking about H atom.

I said 19 century because during that period Hamilton developed his mathematical tools such Hamilton equations and so on... Obviously not only him.

Systems that we observe are usually stable, so the "assumption" comes from the observation, it is an empirical fact! And we don't need QM to assert this.

If you think a bit i was the "theoretical" instability of H atom that made Bohr and Sommerfield to introduce the quantized orbit.

QM is built on Observation, i.e. a System is described by its Observables!

Marco

 

[snapback]

Hi marco,

no problem about the English.. I think each of us two is missing the other's point, but to circumvent this we discuss ;-) ...

You wrote:

If you think a bit i(t) was the "theoretical" instability of H atom that made Bohr and Sommerfield to introduce the quantized orbit.

I want so see an "explanation" of the so called "quantized orbit" in physical terms: charges, forces, moving things, rotating things, whatsoever.

I stated this question already before: why does the electrostatic attraction of opposite charges lead to an annihilation in case of electrons and positrons but not in case of electrons and proton. At long distances the force between the charges is the same in both cases, isn't it ? What makes the difference at short distances ?

Please do not use words like "antiparticle" or "positron is different from proton" to discribe the situation at short distances ;-). Please try to argument with notions like "field, force, charge..." ;-)

Cheers & good weekend

 

[ZapperZ]

I stated this question already before: why does the electrostatic attraction of opposite charges lead to an annihilation in case of electrons and positrons but not in case of electrons and hydrogen. At long distances the force between the charges is the same in both cases, isn't it ? What makes the difference at short distances ?

Please do not use words like "antiparticle" or "positron is different from proton" to discribe the situation at short distances ;-). Please try to argument with notions like "field, force, charge..." ;-)

Cheers & good weekend

Electron and hydrogen do not have any electrostatic attraction between them.

Your question is more appropriate to be posted in the High Energy/Particle Physics forum, not here.

Zz.