Proposed neutron interferometer test of some nonlinear variants of wave mechanics

A family of nonlinear variants of the Schrödinger equation was defined by Bialynicki-Birula and Mycielski by adding terms of the form $F\left({\left|\psi \right|}^2\right)$ to the Hamiltonian. It is proposed that this family be tested by observing whether a phase shift occurs when an absorber is moved from one point to another along the path of one of the coherent split beams in a neutron interferometer. If $F$ is $b$ times a logarithmic function, which is the most important case, a null result with apparatus now available would impose an upper bound on $b$ of 1.5×${10}^{-12\mathrm{}}$ eV, more than two orders of magnitude smaller than the bound estimated by the above authors on the basis of the Lamb-shift measurement.