English

ITVOLT: An Iterative Solver for the Time-Dependent Schr\"odinger Equation

Numerical Analysis 2023-06-07 v2 Numerical Analysis Computational Physics

Abstract

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.

Keywords

Cite

@article{arxiv.2210.15677,
  title  = {ITVOLT: An Iterative Solver for the Time-Dependent Schr\"odinger Equation},
  author = {Ryan Schneider and Heman Gharibnejad and Barry I. Schneider},
  journal= {arXiv preprint arXiv:2210.15677},
  year   = {2023}
}

Comments

The updated version focuses exclusively on the time-dependent Schr\"{o}dinger equation and includes both a new variant of the method and a more rigorous performance analysis. Contents: 20 pages, 5 figures, 2 tables

R2 v1 2026-06-28T04:40:10.104Z