Obtaining the angular momentum state of two spin 1/2 particles for (S=0)

[slimjim]

Homework Statement

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)

Homework Equations

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 textbook, but I don't understand how this particular combination of up/down states is acquired.

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 ] ?

 

[TSny]

Welcome to PF!

Can you show that the state |s = 0, m = 0> must be orthogonal to |s = 1, m = 0>?