Exploring the 2-D Bateman dual system Hamiltonian: a first approach

Dissipation is of major interest in physics and engineering in all energy scales and, hence, it devoted a large amount of investigation. For quantum systems, an usual model for study is the Bateman dual system. Here we use the same model to explore dissipation in angular momentum instead of energy. For that matter, we start with an effective 2-D Bateman model in polar (cylindrical) coordinates and we find the expression for the Hamiltonian. Two constants of motion are found related to modified angular momenta and we test if they are in involution with the Hamiltonian, i.e., if they are integrals of motion. This is in order to verify that the corresponding quantum versions of these constants are good candidates to be a complete set of commuting observables.