A complete spectral characterization of the double commutation method
The Schrödinger operator \(-d^ 2/dx^ 2 + V(x)\) on the line \(\mathbb{R}\) or on the halfline \((0, \infty)\) and auxiliary operators which appear in the framework of the double commutation method (as a composition of two first order operators) are considered. A complete spectral characterization of the method which introduces eigenvalues into arbitrary spectral gaps of the Schrödinger operator is provided. The main result is unitary equivalence of the double commuted operator, restricted to the orthogonal complement of the eigenspace corresponding to the newly inserted eigenvalues, with the original background operator.
scientific article; zbMATH DE number 483973