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Numerical Methods for the Time-Dependent Schrödinger Equation: Beyond Short-Time Propagators

Schneider, Ryan, Gharibnejad, Heman·2025·Atoms
DOI 10.3390/atoms13080070
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Abstract

This article reviews several numerical methods for the time-dependent Schrödinger Equation (TDSE). We consider both the most commonly used approach—short-time propagation, which solves the TDSE by assuming that the Hamiltonian is time-independent over sufficiently small (time) intervals—as well as a number of higher-order alternatives. Our goal is to dispel the notion that the latter are too computationally demanding for practical use. To that end, we cover methods whose numerical building blocks are shared by short-time propagators or can be handled by standard libraries. Moreover, we make the case that these methods are best positioned to take advantage of parallel computing environments. One of the alternatives considered is a “double DVR” solver, which applies an expansion in a product basis of functions in space and time to obtain a solution (over all space and at multiple time points simultaneously) with a single linear system solve. To our knowledge, and despite its simplicity, this approach has not previously been applied to the TDSE.

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Metadata

Authors
Schneider, R., & Gharibnejad, H.
Venue
Atoms
Publisher
MDPI AG
Published
2025-07-28
Volume
13
Issue
8
Pages
70
ISSN
2218-2004
DOI
10.3390/atoms13080070
Cited by
2
Language
en
Licence
creativecommons.org/licenses/by/4.0/ (vor)
Funders
NSF (MSPRF 2402027)

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Schneider, R., & Gharibnejad, H. (2025). Numerical Methods for the Time-Dependent Schrödinger Equation: Beyond Short-Time Propagators. Atoms. https://doi.org/10.3390/atoms13080070

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