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

TL;DR

This paper constructs and analyzes time-dependent rationally extended Pöschl-Teller potentials using exceptional orthogonal polynomials, providing exact solutions and physical insights into their properties under oscillating boundary conditions.

Contribution

It introduces a novel method to obtain exact solutions for time-dependent Schrödinger equations with extended potentials using exceptional orthogonal polynomials.

Findings

Exact solutions for oscillating boundary conditions

Comparison of physical quantities between potentials

Insights into energy and probability distributions

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 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.