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 Schrodinger equation. Such additional terms of the form tbF(lt/i~') 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 F =b in~lb~', we find that the free-space propagation of' slow neutrons places a very stringent upper limit on the magnitude of b. 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 b & 3.3)(10 " eV about 3 orders of magnitude smaller than the lower bound proposed by the above authors.

The scalar version of the Aharonov-Bohm effect predicts a phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space. Unlike the more familiar effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. Rather than using electrons acted on by electrostatic potentials, we have performed an analogous interferometry experiment with thermal neutrons subject to pulsed magnetic fields. The expected phase shifts have been observed to a high degree of accuracy.PACS numbers: 03.65.Bz, 42.50.-p In classical electrodynamics, potentials are merely a convenient mathematical tool for calculating electromagnetic fields of force. In quantum mechanics, however, potentials have a primary physical significance and are an essential ingredient which cannot be readily eliminated from the Schrodinger equation. In a paper entitled "Significance of Electromagnetic Potentials in Quantum Theory" published in 1959, Aharonov and Bohm [1] proposed two types of actual electron interference experiments aimed at exhibiting these conclusions. The phenomena predicted came to be known as the AharonovBohm (AB) effect, and have given rise to a literature of almost 400 journal articles over the last thirty-odd years.The essence of the AB experiments [2] is that electrons suffer phase shifts in passing through regions of space of zero fields but nonzero potentials. The effects are of two types, the usual magnetic (or vector) AB effect, and the less often cited electric (or scalar) AB effect which is conceptually quite simple. It concerns the phase shift caused by the scalar potential V= -eU in the Schrodinger equation:(H 0 +V)yr=ihdifr/dt.(1) Figure 1 (a) shows a divided electron wave packet traveling down two conducting cylinders which act as Faraday cages, i.e., have a field-free interior irrespective of their electrostatic potentials U\ and Ui* To exhibit the scalar AB effect, the potential of cylinder 2 alone is pulsed during a time when the wave packet is contained inside it. In spite of the absence of a force at all times, a relative phase shift A# is expected, A = (\/h)feU 2 (t)dt.(2)The correctness of this AB prediction is of such importance to the consistency of quantum mechanics [3] that the actual experiment deserves a serious attempt. However, such an experiment has not yet been performed because of technical difficulties with existing types of electron interferometers. The closely related experiment of Mateucci and Pozzi [4] involves forces acting on the electron and is not, therefore, a clear-cut test of the effect. Realizations with protons or ions are hindered by the lack of suitable interferometers for such particles.In the present experiment with neutrons, the phase shift is due to a scalar potential, V s -JI * B, which is the analog of V*= -eU, the scalar potential in the scalar AB effect for electrons. (This parallels a previous situation in which th...

A range of phenomena similar or analogous to those of classical optics is exhibited by slow neutrons. The aim of this review is to discuss this similarity and to display the results obtained in a wide range of experimental work on reflection, refraction, diffraction and interference of neutrons.The motivation of such experiments is discussed in the introductory section. The review is divided into three main sections: geometrical optics, wave optics and crystal optics; with subsections that parallel the typical textbook development of classical optics. Special emphasis is placed on the recent developments in neutron interferometry and on the fundamental tests of quantum-mechanical principles made possible by these novel techniques.

We exhibit a specific implementation of the creation of geometrical phase through the state-space evolution generated by the dynamic quantum Zeno effect. That is, a system is guided through a closed loop in Hilbert space by means a sequence of closely spaced projections leading to a phase difference with respect to the original state. Our goal is the proposal of a specific experimental setup in which this phase could be created and observed. To this end we study the case of neutron spin, examine the practical aspects of realizing the ‘projections’, and estimate the difference between the idealized projections and the experimental implementation

of the oscillations in real space is somewhat longer on the trailing edge than on the leading edge. Therefore, interference effects are only observable when the two wave packets are nearly coincident as discussed by Klein, Opat, and Hamilton. 10 To our knowledge, this is the first experiment in which the detailed longitudinal shape of a neutron wave packet has been observed, and the uncertainty relation for neutrons in the longitudinal direction explicitly verified.