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Example case: pairing Hamiltonian

In this basis, the operator ˆP+=ˆa1ˆa2+ˆa3ˆa4+ˆa5ˆa6 From this we can determine that ˆP|1,4,6=ˆP|2,3,6=ˆP|2,4,5=0 so those states all have eigenvalue 0.