Flow Equations for the Henon-Heiles Hamiltonian

Details Flow Equations for the Henon-Heiles Hamiltonian Flow Equations for the Henon-Heiles Hamiltonian

1998-09-29

arxiv.org/abs/quant-ph/9809086v1

Physics

Quantum Physics

latex, 14 pages, 6 figures, uses epsfig, accepted for publication in Physica D

Scientific paper

10.1016/S0167-2789(98)00267-X

The Henon-Heiles Hamiltonian was introduced in 1964 as a mathematical model to describe the chaotic motion of stars in a galaxy. By canonically transforming the classical Hamiltonian to a Birkhoff-Gustavson normalform Delos and Swimm obtained a discrete quantum mechanical energy spectrum. The aim of the present work is to first quantize the classical Hamiltonian and to then diagonalize it using different variants of flow equations, a method of continuous unitary transformations introduced by Wegner in 1994. The results of the diagonalization via flow equations are comparable to those obtained by the classical transformation. In the case of commensurate frequencies the transformation turns out to be less lengthy. In addition, the dynamics of the quantum mechanical system are analyzed on the basis of the transformed observables.

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