تفاصيل الرسالة العلمية

In this thesis, we construct energy-dependent potential models for which the solutions of the Schrodinger equation can be expressed in terms of special orthogonal functions. The method is based on studying various canonical point and gauge transformations applied to a function, g(x), multiplied by a given differential equation of known solutions as special orthogonal functions, that convert it into a Schrodinger-like equation. The method is applied on the confluent hypergeometric differential equation, and various potential forms such as a harmonic oscillator, Coulomb, and Eckart potential, are found. The energy-dependent of the obtained potentials is then implemented. As an application, we search for saturation effect in mass spectra of heavy quarkonia and compare our results with the available experimental results