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

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 X1 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.