Abstract
We analyze the free-space propagation of matter waves with a view to placing an upper limit on the strength of possible nonlinear terms in the Schrödinger equation. Such additional terms of the form were introduced by Bialynicki-Birula and Mycielski in order to counteract the spreading of wave packets, thereby allowing solutions which behave macroscopically like classical particles. For the particularly interesting case of a logarithmic nonlinearity of the form , we find that the free-space propagation of slow neutrons places a very stringent upper limit on the magnitude of . Precise measurements of Fresnel diffraction with slow neutrons do not give any evidence for nonlinear effects and allow us to deduce an upper limit for eV about 3 orders of magnitude smaller than the lower bound proposed by the above authors.
- Received 16 June 1980
DOI:https://doi.org/10.1103/PhysRevA.23.1611
©1981 American Physical Society