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Comparison of the Fourier and Discrete-Variable-Representation Methods in the Numerical Solution of Multidimensional Schrödinger Equations

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Journal of Applied Spectroscopy Aims and scope

Results of numerical solutions of multi-dimensional Schrödinger equations by Fourier and discrete-variable-representation (DVR) methods were compared. Both methods showed comparable accuracy in cases with a smooth potential-energy surface (PES) such as the harmonic 2D PES associated with C=O stretching vibrations in CO2 and the 3D PES associated with vibrations of the donor hydroxyl in the methanol dimer. However, calculations made by the Fourier method were an order of magnitude more time consuming. As applied to unsmooth PES, in particular for an electron in square and hexagonal 2D potential wells with vertical walls (where the Fourier method is inadequate), the DVR method enabled the eigenvalues and wave functions to be calculated.

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Authors and Affiliations

  1. Belarusian State University, 4 Nezavisimost′ Ave., Minsk, 220030, Belarus

    G. A. Pitsevich & A. E. Malevich

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  1. G. A. Pitsevich
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  2. A. E. Malevich
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Correspondence to G. A. Pitsevich.

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Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 82, No. 6, pp. 813–820, November–December, 2015.

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Pitsevich, G.A., Malevich, A.E. Comparison of the Fourier and Discrete-Variable-Representation Methods in the Numerical Solution of Multidimensional Schrödinger Equations. J Appl Spectrosc 82, 893–900 (2016). https://doi.org/10.1007/s10812-016-0200-x

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  • DOI: https://doi.org/10.1007/s10812-016-0200-x

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