Theory and Application of Sturmian Functions

Effective range function below threshold

“…Actually, the solution of the latter below threshold presents a quite simple task thanks to the Sturmian representation of the Coulomb Green's function. The Sturmians, or Sturm-Liouville functions [13,14,15] S ℓν (b, r), where b is a free parameter (Re b > 0) are enumerated by the nodal quantum number ν = 0, 1, 2, ... and result as solution of the differential equation…”

Closed-form solutions of the Schrödinger equation for a class of smoothed Coulomb potentials

“…The values of c i for i < n are then determined in terms of c n by downward recursion using Eq. (9). For j = n − 2, we get…”

“…The approach used in Ref. [1] was somewhat analogous to the Sturmian method [9] for generating a complete basis set of Coulomb wavefunctions, in which the energy E is held fixed and the nuclear charge Z is determined as an eigenvalue. Ref.…”

Pseudo-state Close Coupling in Electron?Atom Collisions

“…The Stieltjes-Tchebycheff imaging-method example presented by Hermann and Langhoff (1983) is a special case of the Fourier series given as pointed out by Stelbovics (1989). Similarly the Sturmian-function expansions as defined by Rotenberg (1970) have Fourier coefficients which he calls Drang functions and presents as power series expansions. These expansions can be identified with the Pollaczeck polynomials discussed here.…”