Identical particles present us with another symmetry in nature.
Electrons, for example, are indistinguishable from each other so we must have
a
symmetry of the Hamiltonian under interchange
of any pair of electrons.
Lets call the operator that interchanges electron-1 and electron-2
.

So we can make our energy eigenstates also eigenstates of . Its easy to see (by operating on an eigenstate twice with ), that the possible eigenvalues are . It is a law of physics that spin particles called

Jim Branson 2013-04-22