I just need some help for a short calculation.
I have to show, that
[tex] (\sigma \cdot a)(\sigma \cdot b) = (a \cdot b) + i \sigma \cdot (a \times b) [/tex]
The Attempt at a Solution
I am quiet sure, that my mistake is on the right side, so I will show you my calculation for this one:
[tex] a_xb_x + a_yb_y+a_zb_z + i\sigma_x (a_yb_z - a_3b_2) + i\sigma_y (a_zb_x-a_xb_z) + i\sigma_z (a_xb_y -a_yb_x) [/tex]
The last 3 terms are a 2x2 matrix and the first 3 terms are just a scalar...
So i can`t add them.
would be happy fora small hint what is wrong :-)