Inverse problem of quantum mechanics for attractive potentials. The discrete spectrum

The dependence of the attractive potentials of a central field on the characteristics of the discrete spectrum of the radial Schrödinger equation for unchanged spectral density of the continuum is investigated. The asymptotic $(r\rightarrow\infty)$ behavior of the corrections to short- and long-range original potentials is analyzed in different cases of changes in the elements of the spectral characteristics.