why triplet state |1,0> is considered "parallel"?
let there be a system of two electrons and thus have s1=s2=1/2 and m1=m2=+-1/2.
the singlet state is:
|0,0> = 1/sqrt(2) ( |1/2,-1/2> - |-1/2,1/2> )
and the triplet
|1,1> = |1/2,1/2>
|1,0> = 1/sqrt(2) ( |1/2,-1/2> + |-1/2,1/2> )
|1,-1> =...