Hamiltonian orderings and functional integrals

The factor ordering problem is discussed using functional integrals and the nonuniqueness of the quantum Hamiltonian is more closely investigated. Systems whose Hamiltonians are quadratic in the momenta are considered in detail and the equivalence of the canonical and Lagrangian approaches is explicitly confirmed by an averaging procedure. It is important that the integrand be in an averaged form if formal manipulations such as partial integrations are to be performed. This is probably significant for perturbation calculations.