  We investigate the evolution of quantal spectra and the corresponding wave
functions along the [O(6)-U(5)]$\supset$O(5) transition of the interacting
boson model. The model is integrable in this regime and its ground state passes
through a second-order structural phase transition. We show that the whole
spectrum as a function of the Hamiltonian control parameter, as well as
structures of all excited states, exhibit rather organized and correlated
behaviors, that provide deeper insight into the nature of this transitional
path.
