Pauli Exclusion Principle: how does an electron know its state?

[Mr Wolf]

This is one of those question you won't find the answer in any book.

From Wikipedia: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers (n, ℓ, mℓ and ms).

But how can an electron know the state (the quantum numbers) of the other electrons, that is, which states are already occupied and consequently occupy an available state?
Or, vice versa, it's the atom that "tells" (how?) the electron the states that are free and that it can occupy?

Thanks.

EDIT: Sorry, I've just noticed the error in the title. It was too long and I had to cut it, but I made a mistake.

 

[blue_leaf77]

But how can an electron know the state (the quantum numbers) of the other electrons, that is, which states are already occupied and consequently occupy an available state?

That's why it's called principle as it cannot be proven, it's just the way how fermions behave.

 

[Mr Wolf]

Thanks for your answer. I was just thinking about a similar answer, that is: it's a principle and that's all.

 

[blue_leaf77]

By the way the shell model of atom is actually based on the independent particle approximation, which means the labeling with four quantum numbers $(n,l,m_l,m_s)$ of each electron is also an approximation. The reason is that the single particle orbital angular momentum operator does not commute with the Hamiltonian, hence the numbers $(n,l,m_l,m_s)$ are not really good quantum numbers for many electron atoms. The actual good quantum numbers are found by finding observables that commute with the Hamiltonian and there should be 4N of such observables (and hence good quantum numbers) with N the number of electrons.

 

[craigi]

This is one of those question you won't find the answer in any book.

From Wikipedia: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers (n, ℓ, mℓ and ms).

But how can an electron know the state (the quantum numbers) of the other electrons, that is, which states are already occupied and consequently occupy an available state?
Or, vice versa, it's the atom that "tells" (how?) the electron the states that are free and that it can occupy?

Thanks.

EDIT: Sorry, I've just noticed the error in the title. It was too long and I had to cut it, but I made a mistake.

The electrons don't "know" each others state. They are both excitations of the electron field, which cannot be in a state which doesn't obey the PEP.

Try this for a start:
https://en.wikipedia.org/wiki/Quantum_field_theory

 

[bhobba]

They are excitations of the same field and the laws governing such fields says they can't have the same state:
http://www.worldscientific.com/worldscibooks/10.1142/3457

Its a very deep theorem that took quite a while to fully sort out.

Thanks
Bill

 

[Mr Wolf]

Thanks for your answers.

I studied many of these things some years ago. So, perhaps I was too naive to look for a simple answer.

 

[bhobba]

So, perhaps I was too naive to look for a simple answer.

There is no simple answer.

Thanks
Bill

 

[Mr Wolf]

I know. That's why I dropped Physics. But, sometimes, old memories come to my mind.

 

[bhobba]

I know. That's why I dropped Physics. But, sometimes, old memories come to my mind.

Perseverance counts for a lot

Thanks
Bill

 

[Mr Wolf]

Yeah, but it's the Math behind that discourages ...and too much Maths burns out the brain.

Ok, later I'll open another thread. I'll try not to be too naive.