  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.
