Quasiclassical approximation with the centrifugal potential excluded

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].