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- Is there any link between principal quantum number and symmetry ?

Hi all,

Group theory show us that irreducible representation of SO(3) have dimension 2j+1. So we expect to see state with 2j+1 degeneracy.

But does group theory help to understand the principle quantum number n ? And in the case of problems with SO(3) symmetry does it explain its strange link with j :

$$n>j $$

?

(I well aware that n and n>j come "easily" with classic solving of the Hamiltonian I just want to know the limit of the group theory in this case).

Group theory show us that irreducible representation of SO(3) have dimension 2j+1. So we expect to see state with 2j+1 degeneracy.

But does group theory help to understand the principle quantum number n ? And in the case of problems with SO(3) symmetry does it explain its strange link with j :

$$n>j $$

?

(I well aware that n and n>j come "easily" with classic solving of the Hamiltonian I just want to know the limit of the group theory in this case).

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