Main Question or Discussion Point
Hello! I am reading Griffiths and I reached the Degenerate Time Independent Perturbation Theory. When calculating the first correction to the energy, he talks about "good" states, which are the orthogonal degenerate states to which the system returns, once the perturbation is gone. I understand mathematically how it works as you need to find simultaneous eigenfunction for the unperturbed Hamiltonian and for the perturbation itself. I am confused from a physics point of view, why would nature favor one orthonormal combination over the other. As in the non-perturbed state all the combinations have the same energy, I would be tempted to believe that once the perturbation is gone, all the states are equally likely. Why isn't this the case (I would prefer some physics insight rather than math, but any answer would be really appreciated)?