A differential equation for the calculation of the functions de jost for regular potentials Application to the system e‾+ H(1s) (2011)
The function of Jost Fl is the theoretical concept that allows to study in a unified way the bound, virtual, dispersed and resonant states that can originate in the interactions between two quantum systems. In collision theory the function of Jost Fl plays a very important role, since it relates directly to the dispersion matrix S. In most of the existing methods in collision theory for the calculation of the Fl function, it is first It is necessary to know the regular solution of the treated system, which is obtained via solution of the Schrödinger radial equation, in order to find the Fl function later. With the methodology proposed in this work, a second-order ordinary linear differential equation is obtained whose solution in the Asymptotic limits coincide with the function Fl. The advantage of the present work is that when solving the differential equation, mentioned above, the function Fl can be obtained directly, without having to find the regular solution of the problem. Another advantage is that no matter the initial (real) conditions that are chosen for the solution of the differential equation, the same elements of the S matrix are always obtained. As an example and test of the methodology, said differential equation is solved numerically, for the elastic dispersion of electrons by hydrogen atoms in the base state at low energies (e− + H (1s)), obtaining for this system the function Fl, the elements of the matrix S and the phase shifts, the latter are compare with those calculated by Klaus Bartschat