  Darboux's theorem guarantees the existence of local canonical coordinates on
symplectic manifolds under certain conditions. We demonstrate a general method
to construct such Darboux coordinates in the vicinity of a fixed point of a
noncanonical Hamiltonian system via normal form expansions. The procedure
serves as a tool to naturally extract canonical coordinates and at the same
time to transform the Hamiltonian into its Poincare-Birkhoff normal form. The
method is general in the sense that it is applicable for arbitrary degrees of
freedom, in arbitrary orders of the local expansion, and it is independent of
the precise form of the Hamiltonian. The method presented allows for the
general and systematic investigation of noncanonical Hamiltonian systems in the
vicinity of fixed points, which e.g. correspond to ground, excited or
transition states. As an exemplary field of application, we discuss a
variational approach to quantum systems which defines a noncanonical
Hamiltonian system for the variational parameters and which directly allows to
apply transition state theory to quantum mechanical wave packets.
