Pauli Exclusion across the three Generations

  • Thread starter TestTubeGames
  • Start date
  • Tags
    Pauli
In summary, fermions and bosons have different properties when it comes to occupying the same state. While fermions cannot exist in the same state, bosons can. This applies to identical particles, but not to particles of different flavors. Using creation and annihilation operators, it can be shown that fermions of different flavors can coexist in the same atom.
  • #1
TestTubeGames
11
0
Fermions are well known for NOT being able to exist in the same state, whereas bosons can. Hence why once an S orbital in an atom has two electrons (with opposite spins), that's it.

But I've only ever seen this discussed for a single type of particle at a time. For instance, could a muon and an electron exist in the same state? Now, I realize this is a bit hand-wavy, since the orbital energies of a muon would (I suppose) be different than an electron... but imagine they weren't. Would there be any restriction to a muon and electron in an atom sharing all 4 quantum numbers?

This would mean that so long as you had a bunch of different types of fermions (muons, taus...) they could 'overlap' like bosons. This seems strange to me. Or am I missing something?

Thanks!
 
Physics news on Phys.org
  • #2
Nope, no problem at all with particles of different flavour occupying the "same" state because as you say, they are different particles, and so they are NOT in the same state. The exclusion principle is only concerned with identical particles, and being of different flavours means two particles are not identical. So yes, in principle you could have a whole set of muon orbitals sitting alongside your electron orbitals in some atom, even if muons and electrons had the same masses and muons were stable.
 
  • #3
Are you familiar with fermionic creation and annihilation operators?
 
  • #4
Thanks to both of you for clearing my head about this issue. I am familiar with the operators you speak of, and from a QM perspective it seems pretty clear. (You can swap two electrons and take into account what happens to the wave function, but not two distinct particles).

I was doubting myself, though, because that flies in the face of those common (and oversimplified) adages. 'Fermions hate being together,' 'bosons can share a room, but fermions don't wanna' ...

Of course, you can't expect total accuracy in such explanations, but I guess some part of my instinct was still based on those anthropomorphized particles I learned about as a kid.

Thanks for setting me straight!
 
  • #5
I asked for the creation and annihilation operators b/c of the following reason: you can create single-fermion states |S> using an operator

[tex]|S\rangle = a^\dagger_S|0\rangle[/tex]

where S means an index S = {momentum, spin, ...} with all other quantum numbers such as flavor and color.

Now using these operators you can also create two-fermion states |SS'> for S≠S'

[tex]|SS^\prime\rangle = a^\dagger_S\,a^\dagger_{S^\prime}|0\rangle[/tex]

But for S=S' you get

[tex]\left(a^\dagger_S\right)^2=0[/tex]

which explains algenbraically why you can't create a two-fermion state with two identical particles S=S'. But b/c this holds only for S=S' the Pauli principle does not apply for different particles, i.e. S≠S', i.e. for an electron and a myon with identical momentum and spin.
 
  • #6
Thanks for the clear proof, Tom. That's one thing I've always enjoyed about Quantum Mechanics. In a topic where your intuition can so easily run you astray, the math is surprisingly clear.
 

1. How does Pauli exclusion principle apply to the three generations of particles?

The Pauli exclusion principle states that no two identical fermions can occupy the same quantum state. This applies to all fermions, including the three generations of particles: up and down quarks, charm and strange quarks, and top and bottom quarks. This means that in each generation, there can only be one quark with a specific set of quantum numbers, such as spin and flavor.

2. Why is Pauli exclusion principle important in understanding particle interactions?

The Pauli exclusion principle plays a crucial role in determining the behavior of particles in interactions. It explains why certain particles are stable and why others decay. For example, the stability of protons is due to the fact that they consist of three quarks, each with different quantum numbers, thus avoiding violating the exclusion principle.

3. How does the Pauli exclusion principle affect the structure of atoms?

The Pauli exclusion principle is the basis for the electron configuration of atoms. It states that no two electrons can have the same set of quantum numbers, which determines their location and energy level within an atom. This principle explains why electrons occupy specific energy levels and why the periodic table follows a specific pattern.

4. What are the implications of Pauli exclusion principle in nuclear physics?

The Pauli exclusion principle is essential in nuclear physics, as it explains why the nucleus of an atom can only hold a certain number of protons and neutrons. This is due to the fact that these particles are fermions and must follow the exclusion principle, resulting in a limit to the size of the nucleus and the stability of elements.

5. How does Pauli exclusion principle contribute to our understanding of matter?

The Pauli exclusion principle is a fundamental principle in quantum mechanics that helps us understand the behavior of matter at the subatomic level. It explains why matter has distinct properties and why it behaves differently from other forms of energy. Without the exclusion principle, our understanding of the structure and behavior of matter would be incomplete.

Similar threads

  • High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
Replies
17
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
3K
  • Quantum Physics
Replies
3
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
1K
  • Quantum Physics
Replies
2
Views
714
  • Quantum Physics
Replies
11
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
11
Views
3K
Back
Top