Supersymmetric WKB and WKB phase shifts for the Coulomb potential, the inverse-square potential, and their combinations

In order to assess the accuracy of the supersymmetric WKB (SWKB) approximation for the calculation of phase shifts, the SWKB and WKB (with the Langer modification) phase shifts up to O(ℎ2) are compared numerically to the exact calculations for the Coulomb potential B/r, the inverse-square potential A/r2 and their combinations A/r2 + B/r, which include the Kratzer (A > O, B < O) and inverted Kratzer (A < O, B > O) potentials. For the inverse-square potential both the SWKB and the WKB methods yield the exact phase shifts. For the other two potentials considered, the results show that the SWKB phase shifts are in many cases superior; however, it is found that the l = O WKB Coulomb phase shifts are more accurate for 0.8 < κ < 1.3 with κ = mB/ℎ2k. In addition, the excellent agreement of the SWKB phase shifts up to O(''Plancconstant'' 4) with the exact ones shows that the SWKB series expansion in powers of ℎ is rapidly convergent for the potentials considered. (Author)