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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 H^{0}and H'". Now say I form a linear combination ψ of my (unperturbed) degenerate states. It satisfies

H_{0}ψ = E_{0}ψ.

Assuming it is the "correct" linear combination in the sense that it diagonalizes my perturbation H', I can write

(H_{0}+H')ψ = Eψ,

where E = E_{0}+ΔE. But this is my question: If the relation (H_{0}+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.

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# Degenerate Perturbation Theory

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