Abstract
Hermite–Weber functions provide a natural expansion basis for the numerical treatment of the Schrödinger equation on the whole real line. For the reflection symmetric Hamiltonians, however, it is shown here that the transformation of the problem over the half line and use of a Laguerre basis is computationally much more efficient in a pseudospectral scheme.
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Taşeli, H., Alıcı, H. The Laguerre Pseudospectral Method for the Reflection Symmetric Hamiltonians on the Real Line. J Math Chem 41, 407–416 (2007). https://doi.org/10.1007/s10910-006-9083-z
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DOI: https://doi.org/10.1007/s10910-006-9083-z
Keywords
- Schrödinger operator
- quantum mechanical oscillators
- singular Sturm–Liouville problems on the real line
- spectral and pseudospectral methods
- Laguerre polynomials
- Laguerre collocation points