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An efficient algorithm based on splitting for the time integration of the Schrödinger equation

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Academic year: 2020

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Figure 1: Comparison of the required minimum polynomial degree m as func- func-tion of θ = βτ for Taylor (dashed line) and Chebyshev (continuous line) for different values of error tolerance: tol = 10 −4 , 2 × 10 −7 , 10 −11
Table 1: Relevant parameters of several symplectic splitting methods especially designed to approximate e −i τ H v with one or more substeps of scaled length θ/m = β ∆τ /m
Figure 2: Different approximations to e −iτ βH v, with H given in (38)-(39), v a random vector, β = 1 and τ β = 20 versus the degree of the polynomials, m
Figure 3: Degree m of the polynomials to achieve tolerances tol = 10 −k , k = 1, 2, .
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