A GEOMETRIC ANALYSIS OF THE SCHRODINGER-EQUATION

A geometric analysis, in conjunction with the use of a Riccati differe ntial equation, allows us to express any eigenfunction Psi of the one- electron Schrodinger equation as a Fade approximant, in terms of the c orresponding eigenvalue, quantities derived from a starting function p hi of the proper symmetry designation, and powers ofthe correction fun ction phi to be added to phi in order to generate Psi. A transformatio n of that expression yields an expansion in powers of phi. This expans ion may be truncated to the number of terms deemed appropriate accordi ng to the quality ofthe starting function. The resulting algebraic equ ation may then be solved for phi. The extension of this formulation to many-electron systems is also described. (C) 1998 Elsevier Science B. V.