# How does the Pauli exclusion principle work?

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• BillKet
In summary, the Pauli exclusion principle states that you can't place two identical fermions in the same quantum state. This is because if you do, then they will be indistinguishable and the system will not exist in that state.
BillKet
Hello! I am a bit confused about the mechanism behind the Pauli exclusion principle. From what I read, it is motivated based on QFT arguments (for example if you don't impose antisymmetry of the fermionic wavefunction you get non-locality, or infinitely negative energies etc.) so mathematically it makes sense. However, if you try to place 2 identical fermions in the same quantum state, what exactly is the thing that exerts the force (and hence the pressure) that prevents you to do so. Mathematically if you do that, you get a zero wavefunction, so the state simply doesn't exists, but in an experiment what is actually going on? Thank you!

Delta2
BillKet said:
if you try to place 2 identical fermions in the same quantum state, what exactly is the thing that exerts the force (and hence the pressure) that prevents you to do so

In order to even formulate this question consistently, you would have to specify how you are trying to place 2 identical fermions in the same quantum state. And right there you come up against a problem: if the two fermions are truly identical, i.e., indistinguishable, then by definition you can't manipulate them separately; you can only manipulate them together, as a single 2-fermion system. If you could manipulate the two fermions separately, they wouldn't be indistinguishable, because your ability to manipulate just one and not the other would count as distinguishing them.

And if you can only manipulate the two fermions as a single 2-fermion system, then it doesn't even make sense to talk about "trying to place them in the same state", because you don't have two systems, you only have one. And you can only put that one system into a state that exists. And questions like, for example, why do 2-fermion systems confined to smaller spaces exert higher pressure, are answerable simply by looking at the properties of the states of the 2-fermion system and how the observables of that system behave as the system's state changes.

zonde
BillKet said:
However, if you try to place 2 identical fermions in the same quantum state, what exactly is the thing that exerts the force (and hence the pressure) that prevents you to do so.
Let's say you take a bunch of helium atoms and try to push them together so that they s1 orbitals overlap. Then all electrons won't have available quantum states near helium nucleus and some of them will occupy next available quantum states using up some energy. So you will end up trying to squeeze positively charged helium ions. If you try to take away that extra energy that you put into electrons QM says you can't get it. Electrons won't give up their energy if there are no lower energy levels that they can occupy.
Now let's say you try to squeeze bunch of neutral neutrons. You can't use electromagnetic interactions to squeeze them but of course you can use gravity for that. And again if there are no available quantum states at the lower energy levels of potential well some neutrons will occupy higher energy levels i.e. the system will expand. Well, you can make potential well deeper by adding some more neutrons but you can add them only in next available quantum states which will make the system even larger. And adding particle to the system means that you are putting it in a potential well and you have to take energy away from it in order to do it. So whenever particle can't occupy lower energy state you can't take away any energy because particle simply won't give it up i.e. you can't squeeze the system tighter.

## 1. What is the Pauli exclusion principle?

The Pauli exclusion principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state at the same time. This means that two fermions cannot have the same set of quantum numbers, such as position, energy, and spin.

## 2. How does the Pauli exclusion principle affect the behavior of particles?

The Pauli exclusion principle plays a crucial role in determining the electronic structure of atoms and the properties of matter. It is responsible for the stability of matter, as it prevents electrons from occupying the same energy level and allows for the formation of chemical bonds.

## 3. What is the significance of the Pauli exclusion principle in chemistry?

In chemistry, the Pauli exclusion principle explains the periodic table and the organization of elements into groups and periods. It also determines the chemical and physical properties of elements, such as their reactivity and melting points.

## 4. How is the Pauli exclusion principle related to the Heisenberg uncertainty principle?

The Pauli exclusion principle and the Heisenberg uncertainty principle are both fundamental principles in quantum mechanics. The Pauli exclusion principle states that two fermions cannot be in the same quantum state, while the Heisenberg uncertainty principle states that it is impossible to know the exact position and momentum of a particle at the same time.

## 5. Can the Pauli exclusion principle be violated?

No, the Pauli exclusion principle is a fundamental law of nature and has been observed to hold true in all experiments. Violation of this principle would lead to the breakdown of our understanding of the behavior of particles at the quantum level.

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