Construction of a transmutation for the one-dimensional Schr\"odinger operator and a representation for solutions
Abstract
A new representation for solutions of the one-dimensional Schr\"odinger equation -u"+q(x)u=w2u 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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