The projection of this vector onto an arbitrary direction is quantized. If the arbitrary direction is called z, the quantization is given by: L ^ ^ z Y ℓ ℓ m = ℏ ℏ m Y ℓ ℓ m , where m is restricted as described above. Note that L and L z commute and have a common eigenstate, which is in accordance with Heisenberg's uncertainty principle. Since L x and L y do not commute with L z, it is not possible to find a state that is an eigenstate of all three components simultaneously. Hence the values of the x and y components are not sharp, but are given by a probability function of finite width. The fact that the x and y components are not well-determined, implies that the direction of the angular momentum vector is not well determined either, although its component along the z -axis is sharp.