Nonlinear von Neumann-type equations

Abstract

We review some recent developments in the theory of nonlinear von Neumann equations. We distinguish between the von Neumann equation (which can be nonlinear) and the Liouville equation (which should be linear). Explicit examples illustrate the technique of binary Darboux integration of nonlinear density matrix equations and special attention is payed to the problem of how to find physically nontrivial `self-scattering' solutions.

To be published in "New insights in quantum mechanics", H.D. Doebner, S.T. Ali, M. Keyl, and R.F. Werner, eds. (World Scientific, 1999); 3 eps figures, style goslar.cls included