Time-dependent rationally extended Pöschl–Teller potential and some of its properties

Abstract

We examine time-dependent Schrodinger equation with oscillating boundary condition. More specifically, we use separation of variable technique to construct time-dependent rationally extended Poschl–Teller potential (whose solutions are given by in terms of $$X_1$$ Jacobi exceptional orthogonal polynomials) and its supersymmetric partner, namely the Poschl–Teller potential. We have obtained exact solutions of the Schrodinger equation with the above-mentioned potentials subjected to some boundary conditions of the oscillating type. A number of physical quantities like the average energy, probability density, expectation values, etc., have also been computed for both the systems and compared with each other.