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Efficient finite difference solutions to the time-dependent Schrödinger equation. (English) Zbl 0886.65095
For solving the initial value and time-dependent problem for the Schrödinger equation an expansion of the evolution operator in terms of unitary anti-Hermitian operators is used. The one-dimensional Laplacian is represented by the standard finite difference approximation of second order and the corresponding exponential is calculated exactly by means of Bessel functions. The proposed algorithms are generalized to two spatial dimensions.

65M06Finite difference methods (IVP of PDE)
35Q55NLS-like (nonlinear Schrödinger) equations
Full Text: DOI
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