Search for a nonlinear variant of the Schroedinger equation by neutron interferometry

A slow-neutron interferometer system has been used to test a nonlinear variant of the Schroedinger equation ih partialpsi(r,t)/partialt=(-h2/2m)del2+U(r,t)]psi -b ln(a3vertical-barpsivertical-bar2)psi. If this equation were correct, then, as Shimony has suggested, repositioning an attenuating plate downstream in a neutron beam would produce a phase modification. No measurable phase shift beyond experimental uncertainty was found and an upper limit of 3.4 x 10-13 eV for the energy constant b was established