As described above, quantum mechanics states that components of angular momentum measured along any direction can only take a number of discrete values. The most convenient quantum-mechanical description of particle's spin is therefore with a set of complex numbers corresponding to amplitudes of finding a given value of projection of its intrinsic angular momentum on a given axis. For instance, for a spin- ⁠ 1 / 2 ⁠ particle, we would need two numbers a ±1/2, giving amplitudes of finding it with projection of angular momentum equal to + ⁠ ħ / 2 ⁠ and − ⁠ ħ / 2 ⁠, satisfying the requirement | a + 1 / 2 | 2 + | a − − 1 / 2 | 2 = 1.