PERTURBATIONS INTO HIGH-ORDER WKB SCHEMES FOR SOLVING ONE-DIMENSIONAL QUANTUM-MECHANICAL MODELS

The WKB approximation in its standard form or in its supersymmetric form (SWKB) has been modified in such a way that effects of an external perturbation upsilon can be taken into account. Perturbation corrections are explicitly written down up to the second order in ($) over bar h and the third order in upsilon, high-order terms can be determined by the same procedure. This method is particularly attractive in the case of a shape-invariant unperturbed potential, where all the unperturbed terms of order n > 0 are vanishing. The potentials V = x(4) + x(2) and V = x(6) + 3x(2) are given as examples.