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PERTURB: A special‐purpose algebraic manipulation program for classical perturbation theory
Author(s) -
Fried Laurence E.,
Ezra Gregory S.
Publication year - 1987
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540080417
Subject(s) - perturbation (astronomy) , algebraic number , poincaré–lindstedt method , quantization (signal processing) , algebraic theory , perturbation theory (quantum mechanics) , algebra over a field , quantum , mathematics , computer science , physics , pure mathematics , quantum mechanics , mathematical analysis , algorithm
Classical 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.