EIGENVALUE CORRECTOR FOR SOLVING BOUND-STATES OF MULTICHANNEL SCHRODINGER-EQUATIONS

An eigenvalue corrector is given for solving bound states in multichan nel Schrodinger equations. Using the renormalized Numerov method the m ultichannel equation is integrated from both left and right to the mid dle. The integrations define an approximate solution which is used to calculate the eigenvalue corrector. The eigenvalue corrector formula i s derived from the Newton-Raphson method and accurate to first order i n energy. An iterative calculation using the present corrector has the advantages that the starting energy is not required to be close to a true eigenvalue and that the convergence rate is quadratic. The theory is illustrated using a model two-channel eigenvalue problem. The resu lts obtained here for the multichannel case are generalizations of tho se obtained by Cooley for the one-channel case. When the present itera tive method is combined with the node counting method for locating the energy interval of a desired level, it provides a very powerful metho d for solving multichannel eigenvalue problems.