  A generalized definition of superpotential has proposed, which connects two
one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra
completely and where: 1) energy of factorization equals to arbitrary level of
spectrum of $V_{1}$ and function of factorization is defined concerning bound
state at this level, 2) energy of factorization equals to arbitrary energy and
function of factorization is defined concerning unbound (or non-normalizable)
state at this energy. It has shown, that for unknown superpotential such its
definition follows from solution of Riccati equation at given $V_{1}$. Using
arbitrary bound state in construction of superpotential, SUSY QM methods in
detailed calculations of spectral characteristics have been coming to level of
methods of inverse problem. So, if as starting $V_{1}$ to choose rectangular
well with finite width and infinitely high walls, then we reconstruct by SUSY
QM approach all pictures of deformation of this potential and its wave
functions of lowest bound states, which were obtained early by methods of
inverse problem. Dependence between parameters of deformation for methods of
SUSY QM and inverse problem has found, analysis of behavior of wave functions
and the potential under deformation has fulfilled, a classification has
proposed for zero-points of potential, nodes of the deformed wave functions,
points, where wave functions are not deformed, an analysis of angles of wave
functions leaving from such points has fulfilled. Using unbound states at
arbitrary energy of factorization, we obtain new types of deformations. So,
using only one superpotential, one can join two potentials, which have real
energy spectra with own bound states and without coincident levels.
