ITVOLT: An Iterative Solver for the Time-Dependent Schrödinger Equation

Solutions to the time-dependent Schrödinger equation (TDSE) are important for understanding a variety of phenomena in atomic and molecular physics, yet many common numerical approaches struggle to achieve both accuracy and efficiency on the problem. Motivated by this gap, we have developed a new approach that solves the TDSE via an equivalent Volterra integral equation. By applying a Lagrange interpolation of the integrand, our approach converts the Volterra integral equation to a linear system, which is then solved iteratively. The resulting method, which we call ITerative VOLTerra propagator (ITVOLT), is relatively simple to implement, but capable of solving the TDSE over large step sizes and with high accuracy. In this talk, we derive the method, explore its numerical details, and demonstrate with a few examples that it is capable of outperforming more standard approaches such as the short-iterative Lanczos and fourth-order Runge-Kutta (RK4). While more complex problems require further exploration, we suggest that ITVOLT be considered as a new, front line computational tool for researchers in atomic, molecular, and optical physics.