Numerical solution of the 3D time dependent Schrödinger equation in spherical coordinates: Spectral basis and effects of split-operator technique |
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Authors: | Tor Sø revik,Tore Birkeland,Gabriel Ok&scaron a |
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Affiliation: | 1. Department of Mathematics, University of Bergen, Norway;2. Department of Informatics, Institute of Mathematics, Slovak Academy of Sciences, Slovakia |
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Abstract: | We study a numerical solution of the multi-dimensional time dependent Schrödinger equation using a split-operator technique for time stepping and a spectral approximation in the spatial coordinates. We are particularly interested in systems with near spherical symmetries. One expects these problems to be most efficiently computed in spherical coordinates as a coarse grain discretization should be sufficient in the angular directions. However, in this coordinate system the standard Fourier basis does not provide a good basis set in the radial direction. Here, we suggest an alternative basis set based on Chebyshev polynomials and a variable transformation. |
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Keywords: | 65M70 81V45 |
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