Product of spin functions

greisen

Hi,

I am looking at the product of two spin function (a_1,a_2) where I would like to apply the spin operator S² to them.

1. To express the S² operator I have seen different expressions either expressed as linear combinations of Pauli matrices or expressed as follows
S²=S_1² + S_2²+2*S_z1*S_z2 + S_+S_- + S_-S_+
using the lowering and raising operator as well. So using S² on a single spin function I get

S²|a> = \hbar^2*3/4|a>

my problem how to do it on the product of two spin functions (a_1,a_2)

Any help or advise appreciated.
Thanks in advance