Flow equations for the Henon-Heiles Hamiltonian

The Henon-Heiles Hamiltonian was introduced in 1964 [M. Henon, C. Heiles, A stron. J. 69 (1964) 73] as a mathematical model to describe the chaotic mot ion of stars in a galaxy. By canonically transforming the classical Hamilto nian to a Birkhoff-Gustavson normal form, Delos and Swimm obtained a discre te quantum mechanical energy spectrum. The aim of the present work is to fi rst quantize the classical Hamiltonian and to then diagonalize it using dif ferent variants of flow equations, a method of continuous unitary transform ations introduced by Wegner in 1994 [Ann. Physik (Leipzig) 3 (1994) 77]. Th e results of the diagonalization via flow equations are comparable to those obtained by the classical transformation. In the case of commensurate freq uencies the transformation turns out to be less lengthy. In addition, the d ynamics of the quantum mechanical system are analyzed on the basis of the t ransformed observables. (C) 1999 Elsevier Science B.V. All rights reserved.