# Wigner-Eckart theorem and selection rules

1. Oct 15, 2006

### JohanL

If you have an operator which in spherical tensor language

$$T^k_q$$

are

$$V=T^2_2 + T^2_{-2} + T^2_0$$

you get a selection rule for j'

$$abs(j-k)=< j' <= j+k$$

in my case i start with angular momentum j=1 and k=2 from above so
the possible new states are

$$1=< j' <= 3$$

But the operator is even under parity and the angular momentum states have parity (-1)^j=-1 in my case.
What does this mean for the possible states j=1 can jump to?

from the selection rule above you get that

j=1 to j'=2
j=1 to j'=3

is possible but does the parity consideration remove any of these possibilities?

Last edited: Oct 15, 2006