Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics III: precise classification of irreducible intertwining operators

The detailed classification of intertwining operators of the first order and of really irreducible intertwining operators of the second order of the I, II and III types is presented in this part of the work. This classification is constructed in dependence of kernels structures of these operators and relations between spectra of intertwined Hamiltonians. It was shown earlier that one can construct from such operators any intertwining operator of arbitrary order with the help of chain (ladder) construction. Bibl. – 25 titles.