Title: In the ground state of helium what's the differing quantum number?
Tags: quantum-mechanics;atomic-physics;quantum-spin;pauli-exclusion-principle
Question: In the ground state of the helium atom, both the electrons have the same quantum numbers $(n,l,m)$ equal to $(1,0,0)$. By Pauli's exclusion principle, the fourth quantum number must be different. What is this fourth quantum number when the electrons are actually in an antisymmetric entangled spin-singlet state?


Here is the accepted answer: The spin. Nothing more and nothing less. The fact that the electrons occupy an entangled spin singlet is the natural consequence of the antisymmetrization required by the Pauli exclusion principle when it is applied to two electrons on states that differ only by their magnetic quantum number. 

Comment for this answer: Yes. The antisymmetrized version of that.
Comment for this answer: $m_{s_1}=+1/2$ and $m_{s_2}=-1/2$?


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