The possible conection between q-defomed hamornic oscillator formation and anharmonicity

In our previous article, the connection between q-deformed harmonic oscillation and Morse-like asymmetric potential is investigated. In present work, a possibility of the connection between q-deformed harmonic oscillator and anharmonic symmetric potential is in detail considered. For simplicity, we take the inverse square cosine-hyperbolic form of potential, i.e Poschl-Teller potential. The relation between the deformation parameter q and the set of parameters of anharmonic symmetric potential was found. The correspondence of two types of connections between q-deformed harmonic oscillator with asymmetric and symmetric potentials are discussed.