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Pseudospectral methods of solution of the Schrödinger equation

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Abstract

Several different pseudospectral methods of solution of the Schrödinger equation are applied to the calculation of the eigenvalues of the Morse potential for I2 and the Cahill–Parsegian potential for Ar2 [Cahill, Parsegian, J. Chem. Phys. 121, 10839 (2004)]. The calculation of the eigenvalues for the Woods–Saxon potential are also considered. The convergence of the eigenvalues with a quadrature discretization method is found to be very fast owing to the judicious choice for the weight function, basis set and quadrature points. The weight function used is either related to the exact ground state wavefunction, if known, or an approximation to it from some reference potential. We compare several different pseudospectral methods.

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Author notes

  1. Bernie D. Shizgal

    Present address: Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada, V6T 1Z1

Authors and Affiliations

  1. Institute of Applied Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Z1

    Joseph Q. W. Lo

  2. Laboratoire Diendonné, Université Nice-Sophia Antipolis, Campus Valrose, Nice, France

    Bernie D. Shizgal

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  1. Joseph Q. W. Lo
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  2. Bernie D. Shizgal
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Correspondence to Joseph Q. W. Lo.

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Lo, J.Q.W., Shizgal, B.D. Pseudospectral methods of solution of the Schrödinger equation. J Math Chem 44, 787–801 (2008). https://doi.org/10.1007/s10910-007-9341-8

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  • DOI: https://doi.org/10.1007/s10910-007-9341-8

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