metry between bosons and fermions in field theories, these methods during their development have formed completely independent section in quantum mechanics [@Cooper.1995.PRPLC].

Today, the methods of SUSY QM are a powerful tool for calculation and analysis of spectral characteristics of quantum systems, they have shown as extremely effective in obtaining of new types of *exactly solvable potentials* and in analysis of their properties, in an evident explanation of such unusual phenomena from the point of view of common sense as a *resonant tunneling*, a *reflectionless penetration* (or an *absolute transparency*) of the potentials (differed from the resonant tunneling by that it exists in a whole energy spectrum, where a coefficient of reflection is not only minimal but equals to zero also), *reinforcement of the barrier permeability* and *breaking of tunneling symmetry in opposite directions during the propagation of multiple of particles*, *absolute reflection for above-barrier energies*, *bound states in continuous energy spectra* of systems [@Zakhariev.1993.PHLTA; @Zakhariev.1994.PEPAN].

A number of papers has been increasing every year. Here, I should like to note a fine review [@Cooper.1995.PRPLC], to note intensively developed methods of *Nonlinear (also Polynomial, $N$-fold) supersymmetric quantum mechanics* in ), methods of *shape invariant potentials* with different types of parameters transformations (for example, see ), methods of a description of *self-similar potentials* studied by *Shabat* [@Shabat.1992.INPEE] and *Spiridonov* [@Spiridonov.1992.PRLTA; @Spiridonov.hep-th/0302046] and concerned with $q$-supersymmetry, methods of other types of potentials deformations and symmetries (for example, see [@Gomez-Ullate.quant-ph/0308062]), non-stationary approaches for a description of properties and behavior of quantum systems [@Samsonov.2002.Proc_IM]. One can note papers unified methods of supersymmetry with methods of inverse problem of quantum mechanics, and I should like to mention to nice monogr