QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

Quantum canonical transformations and quantum trajectories II

Ziemowit Domanski

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We present the general theory of canonical transformations of phase space coordinates in quantum mechanics. The theory is developed within a context of phase space quantum mechanics, which seems to be the most natural approach to quantization, allowing a straightforward development of transformations of coordinates in a complete analogy with classical theory. Later, we adopt the formalism to standard description of quantum mechanics. Moreover, we show that the presented theory of transformations gives a consistent way of quantizing classical Hamiltonian systems after a canonical transformation of coordinates. On the other hand, quantum trajectories on a phase space can be considered as deformations of classical trajectories and are represented by one parameter groups of quantum canonical transformations, hence can be developed in the frame of our formalism.