A LINEAR ALGEBRAIC-METHOD FOR EXACT COMPUTATION OF THE COEFFICIENTS OF THE 1 D EXPANSION OF THE SCHRODINGER-EQUATION/

The 1/D expansion, where D is the dimensionality of space, offers a pr omising new approach for obtaining highly accurate solutions to the Sc hrodinger equation for atoms and molecules. The method typically emplo ys an asymptotic expansion calculated to rather large order. Computati on of the expansion coefficients has been feasible for very small syst ems, but extending the existing computational techniques to systems wi th more than three degrees of freedom has proved difficult. We present a new algorithm that greatly facilitates this computation. It yields exact values for expansion coefficients, with less roundoff error than the best alternative method. Our algorithm is formulated completely i n terms of tenser arithmetic, which makes it easier to extend to syste ms with more than three degrees of freedom and to excited stares, simp lifies the development of computer codes, simplifies memory management , and makes it well suited for implementation on parallel computer arc hitectures. We formulate the algorithm for the calculation of energy e igenvalues, wave functions, and expectation values for an arbitrary ma ny-body system and give estimates of storage and computational costs.