Consider two particles 1 and 2 and two directions in space a and b. The two particles are in the singlet state: with respect to z, the initial state is |₁₂ = 1/2 (|_{z 1} |_{z 2} |_{z 1} |_{z 2}) .

Express the expectation value of the product (spin 1 projected along direction a multiplied by the spin 2 projected along direction b): S⁽¹⁾_a S⁽²⁾_b = . . .? in terms of Planck's constant and the angle between the vectors a and b, . Show that the probability P (a, b) of finding spin 1 along a and spin 2 along b is given by: P (a, b) = a b