Why do bosons and fermions exist?

Question

if i have two particles in states: |1> and |2> respectavly , and they are not identical then the combined state is |1>|2> , but if they are identical then the labels 1 or 2 are arbitrary and could be swapped so supposedly we get two options:

bosons = |1>|2> + |2>|1>
fermions = |1>|2> - |2>|1>

Why there are only these two options ? can't you have any arbitrary superposition of the two states ? (eg: a|1>|2> + b|2>|1> , a*a + b*b = 1)

This is also kinda covered in the Wikipedia entry on identical particles. — Kyle Kanos, Oct 14 '15 at 20:05
Possible duplicate of Why must fermions be antisymmetric? It is not a result of nonrelativistic quantum mechanics. — , Oct 14 '15 at 20:06
wikipdia says that it is just a fact of life that all particles are either bosons or fermions. — user47376, Oct 14 '15 at 20:10
Let's not propose this as a duplicate of a closed question, @NeuroFuzzy. Other possibly-related questions include http://physics.stackexchange.com/q/77950/44126, http://physics.stackexchange.com/q/4049/44126 — rob, Oct 15 '15 at 00:02

score -1 · Answer 1 · answered Oct 14 '15 at 20:09

-1

Wikipedia states:

It appears to be a fact of nature that identical particles do not occupy states of a mixed symmetry.

answered Oct 14 '15 at 20:09

user47376

119

Why do bosons and fermions exist?

1 Answers1