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Gradient Symplectic Algorithms for Solving the Schroedinger Equation with Time-Dependent Potentials

S. A. Chin·C. R. Chen
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Abstract

We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki's method of implementing time-ordering of operators, produces a new class of powerful algorithms for solving the Schroedinger equation with time-dependent potentials. When applied to the Walker-Preston model of a diatomic molecule in a strong laser field, these algorithms can have fourth order error coefficients that are three orders of magnitude smaller than the Forest-Ruth algorithm using the same number of Fast Fourier Transforms. When compared to the second order split-operator method, some of these algorithms can achieve comparable convergent accuracy at step sizes 50 times as large. Morever, we show that these algorithms belong to a one-parameter family of algorithms, and that the parameter can be further optimized for specific applications.

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S. A. Chin, C. R. Chen. 2002-03-05. Gradient Symplectic Algorithms for Solving the Schroedinger Equation with Time-Dependent Potentials. https://doi.org/10.1063/1.1485725

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