ASYMPTOTIC (SEMICLASSICAL) EQUIVALENCE FOR SCHRODINGER-EQUATIONS WITHSINGULAR POTENTIALS AND FOR RELATED SYSTEMS OF 2 1ST-ORDER EQUATIONS

The asymptotic equivalence of systems of two ordinary first-order line ar differential equations with complex independent variable and a smal l parameter at the derivatives is analyzed in the case of arbitrary nu mbers and multiplicities of turning points and singular points. The se t of all the transformation matrices realizing the equivalence is desc ribed and a recursive procedure for constructing these matrices is dev eloped. By persistently using the determinant properties of the transf ormation matrices, the number of integration operations at each step o f this procedure is halved compared with the algorithms known before. The theory is specialized to the case of time-independent one-dimensio nal Schrodinger equations with singular potentials, Some generalizatio ns to multichannel Schrodinger equations are also presented.