Exclusion principles for fermions and bosons

[Brandon1994]

Hello,
I was curious about how the exclusion principle applied to fermions and bosons differently. My current understanding is that the exclusion principle states that no two fermions may be in the same state of motion and that bosons do not obey the exclusion principle. My problem with this is can't two electrons (identical fermions) be in the same state of motion? I know that no two electrons may be described by the same four quantum numbers in the same atom, however, isn't it possible for two electrons in different atoms ( or for the sake of argument two free electrons ) to be in the same state of motion? How does this not violate the exclusion principle?


~thanks

 

[mfb]

They cannot be identical in all quantum numbers. They can have the same spatial wave function ("state of motion"?), if their spin is different, for example.

Electrons are identical - if you consider two atoms, you cannot say "this electron is at atom A and that electron is at atom B". The eigenstates are always combinations of "orbital at atom A" + "orbital at atom B" (plus some modification if the atoms are close to each other), and both electrons will be in different eigenstates.

 

[Brandon1994]

Im not that up on quantum theory ( I am starting college as a physics major and have only completed ap level high school physics and single variable calculus ) but if I understand correctly, you are saying that two electrons are in different states of motion due to the fact that they are in different orbitals? (Im guessing the eigenstate function involves the orbital)