Speculation on Bound Wavefunction Humps as Information

It is known that a quantum bound state wavefunction may have humps which are linked to the energy state n (e.g. a particle in a box with infinite walls or an oscillator). W(x)W(x) (bound) represents a probability distribution. For a fixed variance, a Gaussian distribution maximizes entropy. This is the wavefunction of the ground state of an oscillator, but adding structured phonons not only increases the energy of the state (i.e. moves it from the ground to an excited level), but gives structure (humps) to the distribution. We argue that these humps represent information about the way in which the state may decay. Thus quantum bound states differ from maximized entropy states subject to an overall constraint linked to say energy etc. There seems to be a correlation between higher energy and spatial information which ultimately follows form the momentum-spatial part of the classical action:  px (from -Et+px) being held constant.