PERTURB: A special‐purpose algebraic manipulation program for classical perturbation theory

Abstract

AbstractClassical perturbation theory provides a particularly promising route to EBK quantization of nonseparable systems. However, the number of terms generated when implementing perturbation theory for systems with more than two degrees of freedom can prove too large for general purpose symbolic manipulators to handle. We describe PERTURB, a specialized algebraic manipulation program written in C for quantization of multidimensional systems. A review of operator based classical perturbation theory is given, and the relationship between this type of perturbation theory and quantum mechanical Van Vleck perturbation theory discussed. The relative performance of the Dragt–Finn and Lie transform algorithms is assessed.