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One of Niels Bohr's main contributions to Physics
was his assertion (backed up by experiment) that
angular momentum is quantized -
it can only occur in integer multiples of 
.
Erwin Schr´'odinger showed why this was true for
the wave functions of the hydrogen atom, but by that
time Bohr's principle had been elevated to an empirical
``law'' of Physics that went well beyond the realm of atoms.
Schr´'odinger also showed the peculiar nature of the
quantization of 
: first, its magnitude obeys
where
can only have integer values from zero to
, n being the principle quantum number
for which 
in the case of hydrogen;
second, its projection onto the z axis obeys
where 
can take on
only integer values from 
to 
.
Note that Bohr's original prescription for angular
momentum quantization (integer multiples of 
)
is actually applicable to the z component
of 
- its projection
onto the z
quantization axis, which is chosen arbitrarily
unless there is a magnetic field applied, in which case
is always chosen along the field,
.