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

'A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.'