Solution to the initial value problem for the quantum nonlinear Schrodinger equation.

The quantum nonlinear Schrodinger equation provides an integrable quantum field theory that has been solved by a number of methods. Most recently Gutkin has developed an intertwining operator technique for obtaining the time evolution of the field operators. Using Gutkin's formalism we show how to obtain the exact time evolution of an initial Schrodinger state vector. As an example, the two particle case is carried out explicitly. Numerical results for the time evolution of the position probability distribution are presented for the case when the two particles initially occupy the same Gaussian wave packet. The potential application of the formalism to the propagation of photons through optical fibers is also discussed.