  This paper is a generalization of previous work on the use of classical
canonical transformations to evaluate Hamiltonian path integrals for quantum
mechanical systems. Relevant aspects of the Hamiltonian path integral and its
measure are discussed and used to show that the quantum mechanical version of
the classical transformation does not leave the measure of the path integral
invariant, instead inducing an anomaly. The relation to operator techniques and
ordering problems is discussed, and special attention is paid to incorporation
of the initial and final states of the transition element into the boundary
conditions of the problem. Classical canonical transformations are developed to
render an arbitrary power potential cyclic. The resulting Hamiltonian is
analyzed as a quantum system to show its relation to known quantum mechanical
results. A perturbative argument is used to suppress ordering related terms in
the transformed Hamiltonian in the event that the classical canonical
transformation leads to a nonquadratic cyclic Hamiltonian. The associated
anomalies are analyzed to yield general methods to evaluate the path integral's
prefactor for such systems. The methods are applied to several systems,
including linear and quadratic potentials, the velocity-dependent potential,
and the time-dependent harmonic oscillator.
