Abstract
We present an operatorial technique that uses Schwinger action principle, by means of quantum canonical transformations. This technique enables us to decouple the Hamiltonian of 3-dimensional time dependent quadratic systems (3D TDQS) with linear terms and to transform it to that of free particles, in order to determine exactly the relative propagator of the system. The study is made in this paper for general 3D systems with 3 hybrid anisotropic and varying coupling terms (containing both of position and momentum components), for 3D systems with one varying hybrid coupling term, and for 3D systems with no coupling terms. Two physically relevant examples are presented to illustrate the concrete application of the general formula obtained in this study, those of charged particles in scalar and vector potentials.
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