ASYMPTOTICS OF RADIAL WAVE-EQUATIONS

The Langer modification is an improvement in the WKB analysis of the r adial Schrodinger equation. We derive a generalization of the Langer m odification to any radial operator. For differential operators we writ e the modified classical symbols explicitly and show that the WKB wave functions with the modification have the exact limiting behavior for s mall radius. Unlike in the Schrodinger case, generally the modified ra dial analysis is not equivalent to the WKB analysis of the full proble m before reduction by the spherical symmetry. (C) 1995 American Instit ute of Physics.