Hi I am reading about Degenerate Perburbation Theory, and I have come across a question. We all know that the good quantum numbers in DPT are basically the eigenstates of the conserved quantity under the perburbation. As Griffiths he says in his book: "... look around for some hermitian operator A that communtes with H0 and H'". Now say I form a linear combination ψ of my (unperturbed) degenerate states. It satisfies H0ψ = E0ψ. Assuming it is the "correct" linear combination in the sense that it diagonalizes my perturbation H', I can write (H0+H')ψ = Eψ, where E = E0+ΔE. But this is my question: If the relation (H0+H')ψ = Eψ holds, then what about any first order correction to the wavefunction due to the perturbation? An example of this is the Helium-atom. Here we find that the good linear combinations are symmetric and anti-symmetric, but they are only correct to zeroth order, right? Best, Niles.