Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions

Vladislav V. Kravchenko

Applied Mathematics and Computation, 2018, vol. 328, issue C, 75-81

Abstract: A new representation for solutions of the one-dimensional Schrödinger equation −u″+q(x)u=ω2u is obtained in the form of a series possessing the following attractive feature. The truncation error is ω-independent for all ω∈R. For the coefficients of the series simple recurrent integration formulas are obtained which make the new representation applicable for computation.

Keywords: Transmutation operator; Transformation operator; Spectral parameter power series; One-dimensional Schrödinger equation; Laguerre polynomials (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:328:y:2018:i:c:p:75-81

DOI: 10.1016/j.amc.2018.01.037

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