Equivalence of integral and differential methods of generating accurately solvable potentials of the steady Schroedinger equation

It is proven that the well-known nonlocal (i.e., based on integral transformations) methods of generating accurately solvable potentials of the one-dimensional steady Schroedinger equation are equivalent to multiple use of the local (i.e., based on a differential transformation) method known as the Darboux transformation. New accurately solvable potentials with a hydrogen-like spectrum are obtained, and several functions of the lowest states of the discrete spectrum are presented