ITVOLT: An Iterative Solver for the Time-Dependent Schr\"odinger Equation
Ryan Schneider, Heman Gharibnejad, and Barry I. Schneider
TL;DR
This paper introduces ITVOLT, a new iterative solver for the time-dependent Schrödinger equation that transforms it into a Volterra integral equation and solves it efficiently through global interpolation and linear systems.
Contribution
The paper presents a novel iterative method converting the TDSE into a Volterra integral form, enabling efficient numerical solutions with improved accuracy.
Findings
Effective in solving the TDSE for various examples
Demonstrates improved computational efficiency
Provides detailed numerical analysis and performance evaluation
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.
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Taxonomy
TopicsNumerical methods for differential equations · Electromagnetic Simulation and Numerical Methods · Model Reduction and Neural Networks