Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions
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摘要
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.
论文关键词：Transmutation operator,Transformation operator,Spectral parameter power series,One-dimensional Schrödinger equation,Laguerre polynomials
论文评审过程：Received 26 December 2016, Revised 28 November 2017, Accepted 21 January 2018, Available online 9 February 2018, Version of Record 9 February 2018.
论文官网地址：https://doi.org/10.1016/j.amc.2018.01.037
