How Can J Be a Fraction in Spectroscopic Notation?

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In the discussion about the ^3D_X state with X=3/2, participants analyze the possible values of S, L, J, and J_z. The spectroscopic notation indicates that J should range from |L-S| to |L+S|, where L is 2 and S is 1. However, confusion arises regarding the fractional value of J, as it seems inconsistent with expected integer values. The conclusion reached is that the problem is flawed, as J cannot be a fraction in this context. This highlights the importance of verifying the accuracy of spectroscopic notation in quantum mechanics.
MariusM
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Homework Statement


Consider a ^3D_X where X=3/2 state.

a) What are the possible values of S, L, J and J_z?

Homework Equations


Spectroscopic notation for this LS coupling is ^YL_J where Y=2S+1. J ranges from|L-S| to |L+S|

The Attempt at a Solution


Since L=2 and S must be equal to 1, how can J be a fraction? Shouldn't J be either 1, 2, 3?
 
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You are absolutely right. The problem is incorrect as it stands.
 
Thanks for helping me clarify this!
 

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