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

• URL: http://arxiv.org/abs/2104.02412v2
• Date: Wed, 15 Sep 2021 15:20:40 GMT
• Title: Applying splitting methods with complex coefficients to the numerical integration of unitary problems
• Abstract summary: We prove that a particular class of conjugates are conjugate to unitary methods for sufficiently small step sizes when applied to problems defined in the group $mathrmSU(2)$. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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