International Journal of Quantum Chemistry

Wilson-Sommerfeld quantization rule revisited

S. Mukhopadhyay, K. Bhattacharyya, R.K. Pathak

Published Jan 1, 2001• 4 citations

Abstract

A fresh look at the origin of the Wilson–Sommerfeld quantization rule has been pursued to gain new insight. The rule is shown to provide states that satisfy several well-known theorems of standard quantum mechanics. A few other useful results and scaling relations are also derived. They emerge to act as nice guiding rules of thumb in the course of rigorous computations. Certain features of true excited-state densities can be understood. Goodness of approximate densities can be assessed. Compressed systems can be studied profitably. A route is also sketched that allows one to retrieve classical trajectories from near-exact energy eigenfunctions for both bound and resonant states by exploiting this rule. Additionally, a discussion on semiclassical perturbation theory is presented emphasizing the asymptotic behavior. Pilot calculations demonstrate the success of the present endeavor under various circumstances. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 113–125, 2001

DOI: 10.1002/1097-461x(2001)82:3<113::aid-qua1019>3.0.co;2-i

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