We develop a modification of the WKB method (the modified quantization meth
od, or MQM) for finding the radial wave functions. The method is based on e
xcluding the centrifugal potential from the quasiclassical momentum and cha
nging correspondingly the phase in the Bohr-Sommerfeld quantization conditi
on. MQM is used to calculate the asymptotic coefficients at zero and at inf
inity. We use the examples of power-law and funnel potentials to show that
MQM not only dramatically broadens the possibilities of studying the energy
spectrum and the wave functions analytically but also ensures accuracy to
within a few percent even when one calculates states with a radial quantum
number n(r)similar to 1, provided that the angular momentum l is not too la
rge. We also briefly discuss the possibility of generalizing MQM to the rel
ativistic case (the spinless Salpeter equation). (C) 1999 American Institut
e of Physics. [S1063-7761(99)01108-7].