LANGER TRANSFORMATION AND MODIFIED MATCHING CONDITIONS IN THE WKB METHOD

It is shown that the Kramers-Langer matching condition in the WKB meth od is not asymptotically exact in calculating wave functions in the su bbarrier region if the orbital angular momentum is l similar to 1. Mod ified matching conditions free from this drawback are obtained; they d epend on l, on the energy E, and on the small-distance behavior of the potential V(r). The precision of the new matching conditions is studi ed in calculating the asymptotic coefficients in the wave function at the origin and at infinity. Some regularities in the behavior of the s emiclassical spectrum for power-law potentials are considered.