The resolvent equation of the one-dimensional Schrödinger operator on the whole axis

The inverse spectral problem of some singular version of one-dimensional Schrödinger operator with explosive factor in finite interval

“…It should be mentioned, here, that one of the first paper tackled the direct and inverse problem of sturm-Liouville differential operators with explosive factor in the half line is Gasymov [9]. In the last time grew the interest of investigation of the boundary value problem by numerical methods e.g [10] presented an approximate construction of the Jost function for some Sturm-Liouville boundary value problem in case qðxÞ ¼ 1 by means of collocation method, in addition, [11] is an application of spectral analysis of one-dimensional Schro¨dinger operators in magnetic field. Also [12,13] are applications of discontinuous wave speed problem on nonhomogeneous medium as in our case.…”

Representation of the Solutions of Boundary-value Problems for the Schrödinger Equation in a Hilbert Space

“…Their investigation is of high theoretical and practical interest. Thus, the free Schrödinger equation and the Klein-Gordon equation, which can be represented in the form of the matrix Schrödinger equation, were investigated in [1], the decomposed system of nonlinear equations and the Schrödinger equation with imaginary coefficients were studied in [2], the Kolmogorov-Petrovskii-Piskunov nonlinear diffusion equation was analyzed in [3], and the Schrödinger magnetic operator was investigated in [4,5].…”