We examine time-dependent Schrödinger equation with oscillating boundary condition. More specifically, we use separation of variable technique to construct time-dependent rationally extended Pöschl–Teller potential (whose solutions are given by in terms of \(X_1\) Jacobi exceptional orthogonal polynomials) and its supersymmetric partner, namely the Pöschl–Teller potential. We have obtained exact solutions of the Schrödinger 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.

我们研究了具有振荡边界条件的时变Schrödinger方程。更具体地说，我们使用变量技术的分离来构造时间相关的合理扩展的Pöschl–Teller势（其解由\（X_1 \） Jacobi例外正交多项式给出）及其超对称伙伴，即Pöschl–Teller势。我们已经获得了Schrödinger方程的精确解，其中上述电势受到某些振荡类型的边界条件的影响。还为这两个系统计算了许多物理量，例如平均能量，概率密度，期望值等，并将它们相互比较。