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Can the higher order corrections to energy be calculated the same way in degenerate perturbation theory as with non-degenerate perturbation theory?

Consider the system given by, $$ H|n\rangle = E|n\rangle$$ where: $H$ is the hamiltonian. $|n\rangle$ is the eigenstate. $E$ is the energy of the eigenstate. Now from non-degenerate perturbation ...