Novel method for WKB analysis of multidimensional systems

The availability of powerful microcomputers with graphics capabilities expands the range of numerical procedures that can be employed for undergraduate use. The use of simple software packages for the evaluation of multidimensional WKB approximate eigenvalues is discussed. Introductory courses in quantum mechanics rarely make use of semiclassical theories, such as WKB, to relate quantum mechanics to classical mechanics. This relationship can be helpful for the student’s understanding of quantum mechanics, and a computer experiment can provide a useful avenue for making the concepts concrete. The major components of the approach involve the use of a package for the integration of differential equations, to treat the classical equations of motion, and a computer‐aided design package to determine the phase integral areas. The codes are not expensive, and all exploit the graphical capabilities of microcomputers, which are critical for visualizing the relationship between classical and quantum ideas.