Parametric-time coherent states in a superintegrable Coulomb-type system

Abstract

In this work, we constructed parametric-time coherent states (CS) for a superintegrable Coulomb-type system using the Feynman path integral formalism. This system corresponds to a deformation-dependent extension of the Kepler–Coulomb potential and exhibits maximal superintegrability governed by an indexing parameter. Using the Duru–Kleinert transformation, we mapped the problem onto an effective four-dimensional isotropic harmonic oscillator in parametric time. This transformation allowed the explicit derivation of the propagator, energy spectrum, and coherent-state wave functions while preserving the underlying symmetry structure. The resulting parametric-time CS satisfied the minimum uncertainty relation in the unsqueezed limit and exhibited non-trivial time-dependent squeezing behaviour. We showed that the deformation parameter controlled both the effective spectral scale and the redistribution of quantum fluctuations, leading to deformation-dependent noise suppression.