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## Homework Statement

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

a) What are the possible values of [itex]S, L, J[/itex] and [itex]J_z[/itex]?

## Homework Equations

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

## The Attempt at a Solution

Since [itex]L=2[/itex] and [itex]S[/itex] must be equal to [itex]1[/itex], how can [itex]J[/itex] be a fraction? Shouldn't [itex]J[/itex] be either [itex]1, 2, 3[/itex]?