Solving for the low-rank tensor components of a scattering wave function

Jacob Snoeijer; Wim Vanroose

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arXiv · 2203.10979

Solving for the low-rank tensor components of a scattering wave function

Jacob Snoeijer·Wim Vanroose

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Abstract

Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it has solutions that are outgoing waves, emerging from the target. We show that these waves can be described by a low-rank approximation. For 2D problems this it a matrix product of two low-rank matrices, for 3D problems it is a low-rank tensor decomposition. We propose an iterative method that solves, in an alternating way, for these low-rank components of the scattered wave. We illustrate the method with examples in 2D and 3D.

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BibTeX RIS

Jacob Snoeijer, Wim Vanroose. 2022-03-21. Solving for the low-rank tensor components of a scattering wave function. https://arxiv.org/abs/2203.10979

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