Quantum and classical phenomenological universalities

The quantum Q2 class of phenomenological universalities (PU) is extended to include exact solutions and minimum uncertainty coherent states of Hulthen, Kratzer-Fues, Tipping and generalized Kratzer-Fues-Tipping oscillators. In the dissociation (quasi-quantum) limit the solutions obtained generate the extended U2 class of PU including West-Brown-Enquist universal growth curve and temporal (spatial) fractal functions widely used in the field of life sciences and physics. It will be shown that the PU concept seems to be a valuable methodology for deriving the new forms of potential energy functions with possible applications in theoretical analysis of molecular spectra.