quantum mechanics - Is resonance an energy eigenstate?

In the particle physics book of Martin & Shaw, they used QM to derive the decay distribution, namely, breit wigner formula. What confused me was that, here they assumed the resonance state $\psi_0$ is an energy eigenstate with energy $E_0$.

But in another quesion of mine Does the Breit–Wigner formula indicate "violation" of energy conservation? @anna v suggested that the resonance does not have a definite mass. Hence it can't be an energy eigenstate. This seems to be a contradiction.