If we are combining the angular momentum from two identical particles, like two electrons
in an atom, we will be interested in the symmetry under interchange of the angular momentum
Lets use the combination of two spin
particles as an example.
We know that we get total spin states of
state is called a triplet because there are
three states with different
state is called a singlet.The triplet state is symmetric under interchange.
The highest total angular momentum state,
, will always be
symmetric under interchange.We can see this by looking at the highest
To get the maximum
, both spins to have the maximum
So the product state has just one term and it is symmetric under interchange, in this case,
In fact, for identical particles, the
symmetry of the angular momentum wave function will alternate,
beginning with a symmetric state for the maximum total angular momentum.
For example, if we add two spin 2 states together, the resulting states are:
In the language of group theory,
when we take the direct product of two representations of the the SU(2) group we get:
Two electrons in a P state.*
* Example: The parity of the pion from .*
Jim Branson 2013-04-22