SEMICLASSICAL QUANTUM-THEORY AND ITS APPLICATIONS IN 2 DIMENSIONS BY CONFORMAL MAPPING

The semiclassical quantum theory is investigated with conformal mappin g to analyze the energy levels for a central force potential in two di mensions. The conformal mapping produces a modification in the effecti ve potential which provides the correct phase for the WKB wave functio n. With this modification in the effective potential the semiclassical quantum theory, the so-called WKB approximation, yields the exact ene rgy spectrum for a central force potential in two dimensions, such as the parabolic potential, the attractive Coulomb potential, and the don or impurity states under a plane magnetic field in a two-dimensional s ystem. Among these, the result for the last one is compared with exper imental results and other numerical results.