ABSTRACT
The most elementary method for the construction of canonical transformation functions associated with parameterized transformations is the direct solution of the differential equations that govern the dependence upon the parameters. The construction of the Green's function in some convenient representation, and an investigation of its singularities thus supply the entire energy spectrum of the system together with automatically normalized and complete sets of wave functions for the energy states. The utility of a partial Green's function construction appears in two general situations, which can overlap. One or more compatible constants of the motion may be apparent from symmetry considerations and it is desired to investigate only states with specific values of these quantities. One may be interested for classification purposes in constructing the states of a perturbed system which correspond most closely to certain states of a related unperturbed system.
