SIP-potentials and self-similar potentials of Shabat and Spiridonov: space asymmetric deformation

Abstract

An appropriateness of a space asymmetry of shape invariant potentials with scaling of parameters and potentials of Shabat and Spiridonov in calculation of their forms, wave functions and discrete energy spectra has proved and has demonstrated on a simple example. Parameters, defined space asymmetry, have found. A new type of a hyerarchy, in which superpotentials with neighbouring numbers are connected by space rotation relatively a point of origin of space coordinates, has proposed.