The "complete state" of an electron

[ExplosivePete]

I am in a quantum mechanics course based on the Griffiths text. When the books talks about the wave function on an electron in a specific state, it refers to the "complete state" of the electron as being the product of the spatial part and the spin part of the wave function. The need to distinguish the two components becomes clear when talking about the exchange force in that two fermions can't be in the same state. Is this necessarily a "complete" representation of the electron, or is it possible that there are other factors that could distinguish electrons from each other?

 

[A. Neumaier]

Is this necessarily a "complete" representation of the electron

yes

 

[jfizzix]

Is this necessarily a "complete" representation of the electron, or is it possible that there are other factors that could distinguish electrons from each other?

If there were other factors that could distinguish the electrons from each other, this would show up experimentally because it would be possible (for example) to have more than two electrons in each orbital of an atom. This would have significant consequences in optics and chemistry, but no such consequences are seen.