GENERALIZED NONLINEAR DOEBNER-GOLDIN SCHRODINGER-EQUATION AND THE RELAXATION OF QUANTUM-SYSTEMS

We propose a new class of nonlinear homogeneous extension of the Doebn er-Goldin Schrodinger equation, valid for arbitrary representations an d operators, chosen in accordance with the investigated physical probl em. We verify that the nonlinearity simulates an environment, thence, the new model leads to simple exact solutions as, for instance, the ti me-dependent squeezed coherent states and a special class of stationar y states that we call pseudothermal, reached after relaxation. We illu strate the use of the new equation with applications to problems such as, the relaxation of a two-level or spin-1/2 system, and of the harmo nic oscillator (HO) or equivalently, the emission-absorption process o f photons in an electromagnetic cavity. Furthermore, in order to compa re solutions for the HO example we introduce two different representat ions in the new equation, one continuous (positional representation) a nd the other discrete (Fock states).