Algorithms for solving the Coulomb two-center problem

New algorithms for solving the Coulomb two-center problem of discrete and continuous spectra in prolate spheroidal coordinates with separation of independent variables are presented. Energy eigenvalues and separation constants, as well as eigenfunctions of the discrete spectrum, are calculated using the secant method and the finite element method (FEM) on an appropriate grid with a real parameter - the distance between the Coulomb centers. At each step of the secant method, eigen solutions of the discrete spectrum are computed using the KANTBP 5M program implementing FEM in the Maple system. For the continuous spectrum problem (at a fixed energy eigenvalue), it is sufficient to solve the eigenvalue problem for the quasianqular equation with respect to the separation constant and use it when solving the boundary value problem for the quasiradial equation with respect to the unknown phase shift and eigenfunction using the KANTBP 5M program. The results of test calculations agree with reference calculations performed by programs implementing alternative methods in FORTRAN with the required accuracy.