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

Abstract

A new representation for solutions of the one-dimensional Schrödinger equation -u"+q(x)u=w^2u is obtained in the form of a series possessing the following attractive feature. The truncation error is w-independent for all real w. For the coefficients of the series simple recurrent integration formulas are obtained which make the new representation applicable for computation.

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References in corpus (2)

• Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions
• A Neumann series of Bessel functions representation for solutions of perturbed Bessel equations

Cited by in corpus (1)

• Supersymmetric generalized power functions