THE QUANTUM DISCRETE SELF-TRAPPING EQUATION IN THE HARTREE APPROXIMATION

We show how the Hartree approximation (HA) can be used to study the qu antum discrete self-trapping (QDST) equation, which - in turn - provid es a model for the quantum description of several interesting nonlinea r effects such as energy localization, soliton interactions, and chaos . The accuracy of the Hartree approximation is evaluated by comparing results with exact quantum mechanical calculations using the number st ate method. Since the Hartree method involves solving a classical DST equation, two classes of solutions are of particular interest: (i) Sta tionary solutions, which approximate certain energy eigenstates, and ( ii) Time dependent solutions, which approximate the dynamics of wave p ackets of energy eigenstates. Both classes of solution are considered for systems with two and three degrees of freedom (the dimer and the t rimer), and some comments are made on systems with an arbitrary number of freedoms.