Exact Quantization Conditions. II

Publisher Website
Google Scholar
Abstract
By employing coordinate transformations, a generalized WKB quantization condition is derived which includes a modified WKB quantization rule and the related higher‐order integrals. It is observed that a necessary condition for the first‐order integral to give an exact quantization rule is the vanishing of the higher‐order integrals. When this condition is satisfied, the resulting quantization condition is of the form of all previously known exact‐quantization rules. The higher‐order integrals are shown to vanish for certain cases of interest. An error in Paper I [C. Rosenzweig and J. B. Krieger, J. Math. Phys. 9, 849 (1968)] is noted and an examination of the higher‐order integrals shows that a proposed quantization rule given there is not exact.