- #1
Tangent87
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I have confused myself with this by reading a combination of Wikipedia, books and my QM notes and I'm afraid I need someone to untangle me please.
Basically what I want to know is, what are the consequences of the Pauli exclusion principle
for the ground state of the helium atom?
Here's my confusion: (a). The Pauli exclusion principle says that two electrons (fermions) must occupy a totally antisymmetric state, thus the ground state wavefunction of the helium atom must be antisymmetric.
(b). However the electrons are identical particles and thus the Pauli exclusion principle says that the antisymmetric expression gives zero. Therefore the the ground state wavefunction of the helium atom must be zero.
(c). Also, the wikipedia article on the Helium atom (http://en.wikipedia.org/wiki/Helium_atom) seems to suggest that the ground state wavefunction of the helium atom must be symmetric (unless I'm misreading it which could well be the case).
I know case (b) is wrong because a zero wavefunction is not normalizable but I can't see the flaw in my logic.
Can anyone help me please?
Basically what I want to know is, what are the consequences of the Pauli exclusion principle
for the ground state of the helium atom?
Here's my confusion: (a). The Pauli exclusion principle says that two electrons (fermions) must occupy a totally antisymmetric state, thus the ground state wavefunction of the helium atom must be antisymmetric.
(b). However the electrons are identical particles and thus the Pauli exclusion principle says that the antisymmetric expression gives zero. Therefore the the ground state wavefunction of the helium atom must be zero.
(c). Also, the wikipedia article on the Helium atom (http://en.wikipedia.org/wiki/Helium_atom) seems to suggest that the ground state wavefunction of the helium atom must be symmetric (unless I'm misreading it which could well be the case).
I know case (b) is wrong because a zero wavefunction is not normalizable but I can't see the flaw in my logic.
Can anyone help me please?