Schrödinger equation solution for q-deformed Scarf II potential plus Pöschl-Teller potential and trigonometric Scarf potential

Abstract

The Schrödinger equation for q-deformed Scarf II potential plus Pöschl-Teller potential and trigonometric Scarf potential was solved using Asymptotic Iteration Method (AIM). The combination of three potentials was substituted into the Schrödinger equation, then we separated the three-dimensional Schrodinger equation into three one-dimensional differential equation, consist of the radial part, polar part and azimuth part. The radial, polar and azimuth part differential equations were solved by reducing them into the hypergeometric intermediaries equation, to further we resolved it using AIM. By using AIM, the energy equation and the variable separation constant equations, λ1 for the polar part and λ2 for the azimuth part were obtained, where both are interrelated between the quantum numbers. The value of energies were calculated numerically using Matlab software, where the increasing in the radial quantum number nr causes increase and decrease in the energy. Radial, polar and azimuth wave functions were defined as hypergeometric functions and were visualized using Matlab software. The results show that the disturbance of Poschl-Teller potential and trigonometric Scarf potential give effect in probability