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

03/21/2022

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by   Jacob Snoeijer, et al.

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Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schrödinger 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.