M3L13c.txt

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So this is a classification.
Let's just focus on the simple examples.
We have discussed electric dipole and magnetic dipole
radiation.
These are induced by vectors.
Remember, a1 is the dipole vector.
For m1, the matrix element was by the angular momentum vector.
So these are vectors.
And that means that presentation of the spherical tensors
or the quantum numbers of spherical tensors
are the same of the Y1 m.

So for type of radiation, whether it's
electric or magnetic, we have now the dipole selection rules,
which pretty much say you add 1 unit of angular momentum
to state b.
Can you reach state a with that?
And these selection rules are that you
can change the angular momentum between initial state
by 0 and 1.
This is the triangle rule.
And delta m can be 0 and plus minus 1
depending on polarization, which we're
going to discuss in a moment.
So in angular momentum, electric and magnetic dipoles
have the same selection rule.
Whereas, when it comes to the question of parity--
we've already discussed that-- that an electric dipole
connects two states of opposite parity,
whereas the magnetic dipole connects
two states of the same parity.
And of course, this comes about because L is a axial vector
and I is a polar vector, which have different symmetry when
you invert the coordinate system.
The one higher multipole transition which we discussed
was the electric quadrupole, E2, and the spherical tensor
operators for the quadrupole transition.
I gave you already the example of,
let's see, xz products of two coordinates
because we went one order higher than the dipole.
They transform as Y2, m.
And therefore, we have selection rules
for quadrupole transitions, which tell us now
that we can change the total angular momentum up to 2
and also delta m can change up to 2 units.
And again, just to emphasize because people get confused
all the time, when we talk about a quadrupole transition,
we mean absolutely positively a transition
where one photon is emitted.
If you fully quantize the field, there
is one creation operator of the photon.
It's one photon which is created.
And this photon carries away the angular momentum