ITVOLT: An iterative solver for the time-dependent Schrödinger equation

Abstract

We present a novel approach for solving the time-dependent Schrödinger 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. Program summaryProgram Title: Iterative Volterra Propagator (ITVOLT)CPC Library link to program files:https://doi.org/10.17632/jzd5xpv6t7.1Developer's repository link:https://github.com/ry-schneider/Iterative_Volterra_Propagator.gitLicensing provisions: MITProgramming language: Modern FortranNature of problem: ITVOLT is a solver for the time-dependent Schrödinger equation (TDSE). More broadly, it can be applied to any problem that can be written as a Volterra integral equation.Solution method: ITVOLT solves a Volterra integral equation representation of the TDSE by reducing it to a linear system via Lagrange interpolation of the integrand. It then solves the system iteratively with one of several iteration schemes.Additional comments including restrictions and unusual features: General subroutines assume that the Hamiltonian for the TDSE being solved can be represented by a symmetric banded matrix whose time-dependent component is some scalar function of time (for example a pulse) multiplied by a fixed matrix.