Numerical solution of a nonlinear Schrödinger equation for neutron optics experiments

We report numerical solution of a Schrödinger equation modified by the nonlinear term b ln|ψ|² as proposed by Bialynicki-Birula and Mycielski. Experiments on the diffraction of cold neutrons at an absorbing straight edge performed earlier had set a very low upper limit on b, the strength of the nonlinearity, and it was the purpose of the present calculations to check the validity of some approximations made in the evaluation of that experiment. The numerical solutions show diffraction both in the usual spatial domain and in the time domain. When compared with the earlier estimates we find agreement within a factor of two.