PHYSICS 220 : GROUP THEORY
PROBLEM SET #3
[1] Construct homogeneous polynomial basis functions of the lowest order for all C4v irreps.
[2] Is C4v simply reducible? Why or why not? If yes, construct all its CGCs.
[3] Find all the SU(2) CGCs for
1
2
⊗1=
1
2
⊕ 32 .
[4] By applying the raising and lowering
operators,
j
j1 j2 j
recursion relation relating m m m±1 , m 1∓1 mj2
1
2
1
1
2
show
the SU(2) CGCs
that satisfy a
j
j2 j
j1
m , and m m ∓1 m .
1
2