Suppression of reflection from the grid boundary in solving the time-dependent Schroedinger equation by split-step technique with fast Fourier transform

TL;DR

This paper introduces a numerical method for solving the time-dependent Schrödinger equation that effectively suppresses wave reflection at grid boundaries, allowing accurate absorption of a broad spectrum of wave lengths.

Contribution

The proposed split-step Fourier transform method uniquely suppresses boundary reflections for a wide range of wave spectra, improving upon existing narrow-spectrum techniques.

Findings

Effective boundary reflection suppression for large wave lengths

Applicable to various parabolic equations

Maintains accuracy across broad wave spectra

Abstract

We present an approach to numerically solving the time-dependent Schroedinger equation and other parabolic equations by the split-step technique with fast Fourier transform, which suppresses the backreflection of waves from the grid boundaries with any specified accuracy. Most importantly, all known methods work well only for a narrow region of incident waves spectrum, and the proposed method provides absorption of any wave whose length is large enough in comparison with the size of absorption region.