Phase loss in WKB waves due to reflection by a potential

We study the WKB method away from the short-wave limit. Incorporating the correct phase loss due to reflection at a classical turning point, in place of the usual choice pi/2, can greatly improve the accuracy of the WKB wave function in the classically allowed region. For a repulsive 1/x(2) potential this leads to far more accurate WKB wave functions that the usual Langer modification of the potential.