Accurate solutions of coupled radial Schrödinger equations

A constructive numerical-analytical method of solving coupled Schrodinger equations is presented when a Hamiltonian is a quadratic form of the momentum and contains a matrix potential energy term, which is, in particular, a superposition of Coulomb and polynomial potentials. A technique for solving coupled radial Schrodinger equations is developed. The method is based on the matching of exact solutions, constructed as algebraic combinations of power series, power functions, and a logarithmic function in the neighbourhood of regular singularity r = 0, and of the asymptotic expansions of solutions in the neighbourhood of irregular singularity r = . This method of matching allows us to calculate accurately eigenvalues with corresponding wavefunctions of a discrete spectrum, in(out)-solutions and an S-matrix for a given value of energy from a continuous spectrum, and resonance states. Wavefunctions derived are expressed in analytical form. The method is applied to solving the Schrodinger equation in the case of a matrix Hamiltonian with Coulomb potential.