Applications of the Wigner function to quantum problems involving angle variables

In this thesis the model of the Quantum Pendulum is studied in the Wigner function representation and in the Density Operator representation. Towards this end a completely solvable auxiliary model is introduced. Several families of solutions of the stationarity equations are found and compared. The advantage of using the Wigner function in the discovery of these solutions is made evident. A simpler approach to the derivation of the evolution equations is developed. Links with Mathieu functions and the Helmholtz equation of classical mathematical-physics are analized.