ON MATCHING CONDITIONS IN THE WKB METHOD

The modified matching conditions for quasiclassical wave functions on both sides of a turning point for the radial Schrodinger equation have been obtained. They differ significantly from the usual Kramers condi tion which holds for the one-dimensional case. Namely, the ratio C-2/C -1 in the subbarrier and the classical allowed regions is not a univer sal constant (C-2/C-1 = 1/2, as usual), but depends on the values of t he orbital angular momentum I, energy E and on the behaviour of the po tential V(r) at r --> 0. The comparison with exact and numerical solut ions of the Schrodinger equation shows that the modified matching cond itions not only make the quasiclassical approximation in the subbarrie r region asymptotically exact within the n --> infinity limit, but als o considerably enhances its accuracy even in the case of small quantum numbers, n similar to 1. The power-law, funnel and short-range potent ials are considered in detail.