Exact solution of two-potential system under same range approximation and its implication

In this paper, exact analytical expressions for the Jost solution and Jost function are derived for motion in the nuclear Manning–Rosen plus the Hulthén potential to study both the bound and scattering state observables. The proton-deuteron and alpha-carbon systems are studied to judge the merit of our approach. Our results are found in reasonable agreement with experimental data.

Investigation of spectrum and scattering function of impulsive matrix difference operators

In this paper, we consider a second-order impulsive matrix difference operators. Using the asymptotic and analytical properties of the Jost function, we investigate eigenvalues, spectral singularities, resolvent operator, spectrum and scattering function of this problem. Finally, we study spectrum and scattering function of an unperturbated impulsive matrix difference equation.

The Jost Solutions: Technical Details

This chapter discusses the technical details of the Jost solutions of the Schrödinger equation. The nonrelativistic quantum mechanical two-body problem can be described in terms of the Jost functions and Jost solutions of the Schrödinger equation. When defined for all complex values of the momentum, the Jost functions contain complete information about the underlying physical system. Compared to the S-function which may have redundant poles, the Jost function is a more fundamental quantity because it does not suffer from ambiguities caused by redundant zeros. The chapter first considers the time-independent radial Schrödinger equation before analyzing the regular solution for the Jost function, the poles of the S-matrix, and the wavepacket approach.