We can fix this: take combinations which do have the needed symmetry:
We can fix this: take combinations which do have the needed symmetry:
Symmetric: (u1d2 + u2d1)/?2
Antisymmetric: (u1d2 - u2d1)/?2
So there are three symmetric states, one with both spins up, one with both spins down, and one with zero net spin projection on the vertical, an S=1 state; and one antisymmetric state with vertical component zero, an s=0 state.
Look at the wave function as a function of x for two identical particles. Once again