Wigner-Eckart theorem and selection rules

  • Thread starter JohanL
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If you have an operator which in spherical tensor language

[tex]
T^k_q
[/tex]

are

[tex]
V=T^2_2 + T^2_{-2} + T^2_0
[/tex]

you get a selection rule for j'

[tex]
abs(j-k)=< j' <= j+k
[/tex]

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

[tex]
1=< j' <= 3
[/tex]

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?
 
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