malcomson
May9-11, 06:33 AM
Hi, I'm revising for an exam and I came across a past paper that has a question on annihilation operators, It asks what happens when acting on a wavefunction with a group of different creation/annhilation operators (all identical fermions..
It's quite simple apart from the fact that it includes both spin up and spin down options and in my notes I only have a simplified case of all spin up fermions.
My question is, if the annihilation operator ai is has the constants (-1)^n1+n2+...+ni-1 times ni where n1 etc are the occupancies of each state. Does this include both spin states of should I treat them as separate sets.
I think I should include both spins as that would give the anticommutation relations between operators of different spins, allowing antisymmetry of a function under the interchange of two particles of opposing spin but I'm not really confident about it.
Apologies if unclear, am yet to figure out putting equations in posts.
It's quite simple apart from the fact that it includes both spin up and spin down options and in my notes I only have a simplified case of all spin up fermions.
My question is, if the annihilation operator ai is has the constants (-1)^n1+n2+...+ni-1 times ni where n1 etc are the occupancies of each state. Does this include both spin states of should I treat them as separate sets.
I think I should include both spins as that would give the anticommutation relations between operators of different spins, allowing antisymmetry of a function under the interchange of two particles of opposing spin but I'm not really confident about it.
Apologies if unclear, am yet to figure out putting equations in posts.