FINITE-DIFFERENCE SOLUTION OF THE COUPLED-CHANNEL SCHRODINGER-EQUATION USING RICHARDSON EXTRAPOLATION

A method for numerical solution of the coupled-channel Schrodinger equ ation for bound states based on the finite-difference method of the se cond order with iterative extrapolation of net eigensolutions is descr ibed. It is shown that Richardson's extrapolation to the limit signifi cantly increases the accuracy of the finite-difference solutions with substantial reduction of requirements in computer memory, disk storage and computational time. The same extrapolational procedure and error estimations are applied to the eigenvalues and eigenfunctions. Results of sample calculations for several quantum-mechanical problems are pr esented and discussed. One of the sample problems considered is the hy drogen atom in a uniform magnetic field.