Consider the parity operator. Acting on the position, it reverses the directions of space, so that PxP = − x. Similarly, it reverses the direction of momentum, so that PpP = − p, where x and p are the position and momentum operators. This preserves the canonical commutator [ x, p ] = iħ, where ħ is the reduced Planck constant, only if P is chosen to be unitary, PiP = i.