We present a novel approach for solving the time-dependent Schr\"{o}dinger equation (TDSE). The method we propose converts the TDSE to an equivalent Volterra integral equation; introducing a global Lagrange interpolation of the integrand transforms the equation to a linear system, which is then solved iteratively. In this paper, we derive the method, explore its performance on several examples, and discuss the corresponding numerical details.

翻译：我们提出了一种求解含时薛定谔方程（TDSE）的新方法。该方法将TDSE转化为等价的Volterra积分方程；通过对被积函数引入全局拉格朗日插值，将方程转化为线性系统，并采用迭代方式求解。本文推导了该方法，探讨了其在多个算例中的性能表现，并讨论了相应的数值细节。