Exact solutions of the Schrödinger equation using extended Nikiforov-Uvarov formalism for generalized pseudo-harmonic oscillator

The Schrodinger equation with generalized pseudo-harmonic oscillator (GPHO) is transformed into a form that is compatible with extended Nikiforov-Uvarov (ENU) formalism, and its exact solutions are obtained in three and N-dimensions using this formalism. The energy spectrum for the GPHO was obtained in closed form, and the wave function was determined using the biconfluent Heun differential equation. Special cases are deduced, and some numerical results are shown to illustrate the behaviour of the bound state energies at different quantum states for various values of potential parameter; lambda. In addition, the thermodynamic property expressions for GPHO are obtained in closed form, and their variation with temperature-dependent parameters is discussed extensively for various values of lambda. Our results agree with those obtained in the literatures.