An improved semiclassical method with reference potentials

Abstract

We approximate given potentials by means of the specially introduced reference potentials. On the one hand their parameters may be easily found from the usual WKB integral for the given potential; on the other hand they allow a simple determination of the first correction to the usual quantization condition. Such reference potentials are introduced in special variables as some Pade approximants which lead usually to a very good results for various problems. Thus we raise the accuracy of the WKB method for a broad set of potentials without cumbersome calculations. Higher order corrections as well as the exact condition is also considered.