Generalized Darboux–Crum–Krein transformations

Expressions are obtained by means of which it is possible to transform a known solution $\varphi_1$ of the Schrödinger equation with potential $V_1$ into a solution $\varphi_2$ with corresponding potential $V_2$ when the Schrödinger equation contains not only a nuclear potential $V$ but also a centrifugal and a Coulomb potential. In special cases, these transformations yield the formulas of a Darboux–Crum–Krein transformation, and also formulas obtained by other authors.