Also, the matrix representations of the x, y, and z components of spin s are given by
0 1/2 0 /2 1/2 0 , , and .
1/2 0 /2 0 0 1/2x y z i
s s s i
-Ê ˆ Ê ˆ Ê ˆ = = =Á ˜ Á ˜ Á ˜-Ë ¯ Ë ¯ Ë ¯
Now, consider a two-electron system and let these electrons occupy the single electron states Y1(t1) and Y2(t2). Because the two-electron wave function F(t1, t2) must be antisymmetric with respect to the permutation of the coordinates of electrons 1 and 2, we choose a Slater determinant for the two-electron wave function, which to a rst approximation is given by
Y t Y t F t t =
Y t Y t 1 1 2 1
( ) ( )1 ( , ) .