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arXiv · 2104.02412

Applying splitting methods with complex coefficients to the numerical integration of unitary problems

S. Blanes·F. Casas·A. Escorihuela-Tomàs
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Abstract

We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr\"odinger equation. We prove that a particular class of integrators are conjugate to unitary methods for sufficiently small step sizes when applied to problems defined in the group $\mathrm{SU}(2)$. In the general case, the error in both the energy and the norm of the numerical approximation provided by these methods does not possess a secular component over long time intervals, when combined with pseudo-spectral discretization techniques in space.

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S. Blanes, F. Casas, A. Escorihuela-Tomàs. 2021-04-06. Applying splitting methods with complex coefficients to the numerical integration of unitary problems. https://arxiv.org/abs/2104.02412

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