NOTE 1 The expectation value of spin in any direction is $\hslash \sqrt{s(s+1)}$ where s is spin quantum number and ħ is reduced Planck constant.

NOTE 2 The spin in a given direction is quantized as multiples or half-multiples of the reduced Planck constant. In the direction of the quantization axis z, the component of the spin is quantized as S_z = m_sħ, m_s = s, s − 1, … − s, where m_s is spin magnetic quantum number and s is spin quantum number.