Symbolic calculations of unitary transformations in quantum dynamics Original Research Article

The present paper deals with the development of a Mathematica package of programs for handling quantum mechanical equations involving commutators and unitary transformations. One program implements general commutators handling rules. Another evaluates a series of nested commutators representing a general unitary transformations. We apply these new symbolic routines to test-transformations, ranging from simple translations in both spatial and momentum spaces to transformations involving nonlinear generators and denoting non-inertial changes of reference frames in the phase space. We illustrate with a simple example how these tools can be used to solve formally a molecular dynamical problem.