I see that in the 1$s$ orbital the electrons have to have different spins, still there is two possible states,
- a singlet state with an anti-symmetric superposition of spins and symmetric spatial part
- a triplet state with symmetric superposition of spins and anti-symmetric spatial part
So, the question reduces to WHY the first one? I have read somewhere else that a ground state has to have a symmetric spatial wave function always but without further reasoning why this should be necessarily true.