NONLINEAR SCHRODINGER-LIOUVILLE EQUATION WITH ANTIHERMITIAN TERMS

We extend a nonlinear dynamical equation, proposed a few years ago by S. Weinberg to test a possible breakdown in the linearity of Quantum M echanics, by introducing antihermitian terms (linear and nonlinear) al lowing irreversible evolution. Applying the new equation to a two-leve l atom, we verify that for a particular situation the antihermitian te rms lead exactly to the nonlinear Bloch equations obtained in the neoc lassical theory of spontaneous emission proposed by Stroud and Jaynes, which do not exhibit pure spontaneous emission. Lifting that particul arization we gain additional antihermitian terms in the nonlinear Bloc h equation that take care of the pure spontaneous emission problem. In view of this new terms we discuss whether they are meaningful as a '' correction'' to linear Quantum Mechanics.