Here we have two identical paticles with spin I, integer or half-integer, and there are (2I+1)2 states.
Each one of them can be uniquely determined by total spin and its orientation, we can use |J,m⟩ to represent this state. And because of its uniqueness, it is either symmetric or antisymmetric.
How to determine whether |J,m⟩ is symmetric or antisymmetric based on I, J and m?
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