Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

A systematic semiclassical expansion of the hydrogen problem about the clas sical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as in the WKB approximation and semic lassical quantization of hydrogen, where the factor l(l + 1) is replaced by (l + 1/2)(2), are avoided. Expanding systematically in powers of (h) over bar, the semiclassical energy levels are shown to be exact to first order i n h with all higher-order contributions vanishing. The wave functions and d ipole matrix elements rue also discussed. [S1050-2947(99)10407-4].