- Historically, the term spin had (and sometimes
has) a narrower meaning than angular momentum. Picture an electron
in an atom. Sacrificing some accuracy on the altar of visual imagery,
think of the electron as orbiting about the nucleus, and spinning on its
axis. The orbital motion gives rise to so-called orbital angular momentum;
the spinning gives rise to so-called intrinsic or spin angular momentum.
- ... momentum2
traditionally stands for orbital angular momentum, and stands for spin
- ... component.3
- People sometimes
use instead of to denote this.
- ... somehow4
- Not so
trivial, because the three component measurements are mutually
incompatible; it is theoretically impossible to measure and
simultaneously (for example). Nonetheless, the combination
- Specifically, Bohr's energy levels agree exactly with
those derived from Schrödinger's equation, when we neglect the spin of
the electron, the spin of the proton, and relativistic effects. (Spin
itself is sometimes considered a relativistic effect.)
- ... above).6
- Sommerfeld gave a single more general quantum
condition which implied the quantum conditions for , , and as
special cases. So Sommerfeld's approach was not so ad-hoc as this summary
makes it look.
- ... model7
- Bohr did not make use of the quantum
number ; instead, he had slots at level (
each capable of holding electrons. Note that this is actually
- ... vector8
- We mean an
ordinary 3-space vector, not a vector in a (complex) Hilbert space.
- ignoring any motion of the proton, a good approximation
- Alfred Landé independently came up with the same
half-integer trick. He did publish, and so attached his name to the
- These lines are responsible for the color of sodium vapor
lamps used on many highways.
- ... spectrum.12
- The sodium D-lines provide
an example. The quartet and the higher doublet both have and
; their 's are and .
- ... ``small''13
- In particular cases, ``small'' and
``slowly'' can be given more definite meaning. For example, we may be able
to write as a power series in something; might contain the second
and higher order terms.