Quantum and classical phenomenological universalities

Abstract

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.