Niejednorodne transformacje symplektyczne w mechanice klasycznej i kwantowej

Abstract

The connection between quantum-mechanical unitary transtormations and canonical transformations of classical mechanics is discussed in the special case of nonhomogeneous symplectic transformations. The discussion is based on the Wigner-Moyal phase - space formulation of quantum mechanics. Explicit form of the Wigner transform of corresponding unitary operator is found and it is proved that only this class of unitary transtormations maps the Wigner functions by a change ot variables.