Comparison between phase space structures in coupled Morse systems and in various su(2) approximations

While Hamiltonians written in terms of position and momentum provide a tran sparent picture of the motion of a system, Hamiltonians written in terms of Lie algebras are easier to handle quantum mechanically. Therefore we are i nterested to know how to transform one into the other. Since the exact tran sformation often leads to complicated expressions, we look for approximatio ns which preserve the essential features. As basic criterion we look for th e degree of equality of the classical phase space structures. We illustrate our ideas for the case of two coupled Morse systems and its approximation in terms of the Lie algebra su(2), which is relevant to anharmonic models o f molecular spectroscopy. (C) 2001 American Institute of Physics.