Question about Pauli exclusion principle

[LostConjugate]

"More generally, no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously."

Now a quantum state can be setup to describe a collection of atoms, or molecules, or the entire universe in one state.

So my question is, two electrons in different parts of the universe can't occupy the same quantum state? How can this be? You can have two hydrogen atoms, each with an electron with the same n,l,m,s quantum numbers.

This also says that out of all the electrons in the universe only 2 at a time can share the same momentum, 1 spin up, and 1 spin down. Since 2 electrons with the same momentum and same spin would be sharing a quantum state.

 

[SpectraCat]

"More generally, no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously."

Now a quantum state can be setup to describe a collection of atoms, or molecules, or the entire universe in one state.

So my question is, two electrons in different parts of the universe can't occupy the same quantum state? How can this be? You can have two hydrogen atoms, each with an electron with the same n,l,m,s quantum numbers.

No, what you are missing is that the relevant Hamiltonian for describing the internal degrees of freedom of the H-atom is referenced to the center of mass coordinates. Thus for two separated H-atoms (assuming a large enough distance that their interaction can be neglected), the Hamiltonians are different. Two particles can't be in the same quantum state if their Hamiltonians are different.

This also says that out of all the electrons in the universe only 2 at a time can share the same momentum, 1 spin up, and 1 spin down. Since 2 electrons with the same momentum and same spin would be sharing a quantum state.

See above ...

 

[LostConjugate]

No, what you are missing is that the relevant Hamiltonian for describing the internal degrees of freedom of the H-atom is referenced to the center of mass coordinates. Thus for two separated H-atoms (assuming a large enough distance that their interaction can be neglected), the Hamiltonians are different. Two particles can't be in the same quantum state if their Hamiltonians are different.



See above ...

Thanks!