Canonical transformation in quantum mechanics

The phase-space picture of quantum mechanics and some examples illustrating it are presented. Since the position and momentum are c numbers in this picture, it is possible to introduce the concept of phase space in quantum mechanics. The uncertainty relation is stated in terms of an area element in phase space, whose minimum size is Planck’s constant. Area-preserving canonical transformations in phase space are therefore uncertainty-preserving transformations. The wave-packet spread, coherent-state representation, and squeezed states of light are discussed as illustrative examples.