I am learning about the wavefunction of two electrons in a Hydrogen molecule and I came across following spin states: |↑↑⟩ and |↓↓⟩, which form two of the triplet states in the molecule.
This confuses me since we are speaking in terms of molecular wavefunctions and not in terms of two different atomic wave functions. That is, we are talking about the combined state of two electrons in terms of |Ψ(x1,x2)⟩ in a molecule, and from my understanding of molecular orbital theory, a molecular orbital must also obey Pauli's exclusion principle. So in that case, shouldn't the spins always point in the opposite directions?
Best Answer
Pauli exclusion forbids more than one fermion in the same state. But what you're writing down in $\lvert \uparrow\uparrow\rangle$ is just the "spin component" of the state - the two electrons still can have different spatial wavefunctions (e.g. one is primarily localized around one of the protons and the other around the other proton) and hence do not share the same state, so Pauli exclusion does not forbid this.