I have heard there is only one component of the atom momentum quantized, (Lx, Ly, Lz) then, does it have an orientation in space?

Asked by: Roberto

Answer

Yes, the angular momentum of an electron in an atom has a quantized orientation in space, though it cannot be determined exactly. Angular momentum is a vector quantity, meaning it has both magnitude and direction, and can be described by three components (in three dimensions).

As a consequence of the Heisenberg uncertainty principle, once we determine the magnitude, only one component can be determined at any time, because determining a second would give enough information to deduce the third and violate the principle that we cannot simultaneously determine the position and momentum of a particle. One way to picture our understanding of the angular momentum vector is as an arrow with a fixed length (magnitude) that makes a fixed angle from the horizontal, but that can rotate freely about the vertical, tracing out the shape of a cone. The one determined component (by convention Lz) is itself quantized, which corresponds to different specific angles from the horizontal, which therefore trace differently shaped cones, representing different quantized sets of spatial orientations.
Answered by: Edward Faulkner, Physics Undergrad, West Point, NY