A comparison of algorithms for the normalization and quantization of polynomial hamiltonians

Abstract

Algorithms and programs for the normalization of polynomial Hamiltonians of classical mechanics by the Birkhoff-Gustavson and Deprit-Hori, as well as quasi-classical quantization procedures for normal forms, are compared. The algorithms and programs are represented in a universal pseudocode and implemented in the computer algebra systems REDUCE, MAPLE, and MATHEMATICA. Examples that illustrate the operation of these algorithms and programs for polynomial Hamiltonians of atomic systems in external electromagnetic fields are considered