# Why the total angular momentum of Helium ground state is 0?

Physics Asked by amilton moreira on December 11, 2020

Every reference I have seen says that the total angular momentum of helium ground state of is zero.

My question is since the the Hamiltonian $$H$$ commutes with the total angular momentum $$J$$ why can we have energy eigenstate of the form $$psi(E,J)=k(E)phi(J)$$ such that we have
$$HK(E)=e_0k(E)$$ $$Jphi(J)=j_0phi(J)$$
such that $$e_0$$ is the ground state energy and $$j_0neq0$$

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