ABSTRACT
Radial and fidif. methods of this chapter are based on finite difference simulations of the Schrodinger differential equation. Both of the methods are based very strongly on an appropriate algebraic analysis, as the text makes clear. The finite difference approximation method described is not the most powerful of the finite difference methods available, but is quite adequate to give accurate energies for the low-lying levels of the Schrodinger equation. For such singular potentials the use of a matrix diagonalization approach is complicated by the presence of divergent matrix elements. One of the most commonly used and cited methods for handling the Schrodinger equation is the Numerov method, which for smooth potentials has a leading error term of h4 type in its energy estimates. Constant potential approximations have also been used in the propagator method of shooting. The literature on finite difference methods is vast; the author’s collection of selected reprints on that topic contains several hundred items.
