What are good books/chapters of books or articles to study canonical transformations in quantum mechanics at a graduate level? I am looking for any kind of sources about canonical transformations in quantum mechanics in the operatorial formulation of the theory and its connection with the classical canonical transformation theory.
 A: I am unaware of many detailed resources in the area targeted towards typical physics graduates. However, there is a CRM monograph dealing with the Function Theory on Symplectic Manifolds which is targeted more towards mathematics graduates. It will of course, be appealing to any physics graduate with an interest in mathematical physics, as one can see from the book's description.

This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards.

A softer introduction to the subject matter may be found here. I quote the abstract below,

Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary transformations for constructing solutions of the Schrödinger equation is discussed. Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can be realized quantum mechanically as a product of these transformations. Each transformation corresponds to a familiar tool used in solving differential equations, and the procedure of solving a differential equation is systematized by the use of the canonical transformations. Several examples are done to illustrate the use of the canonical transformations.

