Hi Guys, this is from my grad quantum class. I'm pretty stuck and need some help: 1. The problem statement, all variables and given/known data Given four spin-1/2 particles, derive an expression for the total spin state |S,m⟩ ≡ |1,0⟩ in terms of the the four bases |+⟩i , |−⟩i ; i = 1,2,3,4 2. Relevant equations Clebsch Gordon Coefficients Raising and lowering operators, etc. 3. The attempt at a solution OK. So I know the solution has to be of this form: [tex]|1,0> = a|+++->+b|++-+>+c|+-++>+d|-+++>[/tex] Now, here is my plan of attack: First, the state [tex]|2,2>=|++++>[/tex] I applied the lowering operator to this state repeatedly to find the [itex]|2,0>[/itex] state. Then I use the condition that: [tex]<1,0|2,0>=0[/tex] to get: a+b+c+d=0 Also, there is the normalization condition: [tex]a^2+b^2+c^2+d^2=1[/tex] So, I have two equations in 4 unknowns. This is my problem. I can find a third equation by considering <0,0|1,0>=0 however, i don't know the form of the singlet configuration for 4 spins. Any hints on how I can find that? Still that leaves me still with 3 equations in 4 unknowns. Where do I get the last equation? Any hints at all would be appreciated. Thanks alot.