1. The problem statement, all variables and given/known data consider the possible angular momentum states |s,m>, of a system of two spin-1/2 particles construct all possible states with total spin zero (S=0) 2. Relevant equations 3. The attempt at a solution if total S of system is zero, m must also equal zero. So the only state is |s=0,m=0> and |s=0,m=0> = 1/sqrt(2)[ up*down - down*up ] I got the exact form of |0,0> from my text book, but I dont understand how this particular combination of up/down states is aquired. considering the state |s=1,m=1>, its intuitive that m can only equal 1 if both spins are +1/2. The same goes for |s=1,m=-1> where both spins are -1/2. Then one can obtain |s=1,m=0> by applying the lowering operator to yield: |s=1,m=0> = 1/sqrt(2)[up*down+down*up) my book gives a thorough explanation i deriving the s=1 states, but then it just gives the S=0 state without much explanation. so how do you obtain |s=0,m=0> = 1/sqrt(2)[ up*down - down*up ] ?