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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Reflection of the de Broglie wave packet from thin films

Vladimir K. Ignatovich, Filipp V. Ignatovich

Published Dec 18, 2000• 0 citations
Publisher

Abstract

Reflection of cold neutrons from thin films, when the free neutron wave function is supposed to be the de Broglie singular wave-packet, is considered. Small corrections to interference pattern for the reflection dependence on the packet width is found. This correction for the case, when the width of the packet extracted from ultra cold neutrons anomaly, is calculated. The correction is shown can also be represented as a small contribution of incoherent reflection from interfaces of the film. The magnitude of this contribution is computed.

DOI
10.1117/12.410550

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Reflection of cold neutrons from thin films, when the free neutron wave function is supposed to be the de Broglie singular wave-packet, is considered. Small corrections to interference pattern for the reflection dependence on the packet width is found. This correction for the case, when the width of the packet extracted from ultra cold neutrons anomaly, is calculated. The correction is shown can also be represented as a small contribution of incoherent reflection from interfaces of the film. The magnitude of this contribution is computed.
Neutron time-of-flight interferometry assumes the validity of the classical time-of-flight expression in the interpretation of time-of-flight data and simultaneously assumes that the incident neutrons are de Broglie wave packets obeying the laws of quantum mechanics. A quantum-mechanical treatment of time of flight as an expected value of an appropriate time-of-arrival operator for a given initial wave-packet state shows that the size of the initial wave packet introduces measurable quantum corrections to the expected classical time of flight. Our results provide concrete testable predictions that may clarify the status of time as a quantum-dynamical observable.
In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. However, it is the transverse spatial extent of packet wavefronts alone that determines the area within which a coherent scattering process can occur in the first place. This picture is shown to be consistent with standard quantum theory. It is also demonstrated that these two measures of coherence can be distinguished from one another experimentally.
The transmission and the reflection of a wave incident on a potential in one-dimensional quantum mechanics are usually discussed by assuming that a plane wave eikx or a broad wave packet is incident. We are interested in what happens if the width of the incident wave packet is very small. In this case, the incident wave packet can spread out in such a way that part of the wave packet turns around before reaching the potential area and proceeds backward. This can clearly be visualized by means of the Bohm trajectories associated with the wave packet. We discuss a complication that arises in this case regarding the notion of the reflection probability.PACS Nos.: 03.65–w, 03.65.Nk
We discuss the formulation of neutron-interferometry experiments in terms of density matrices of plane waves. It is shown that the shape of the interference pattern does not depend upon the off-diagonal terms. As special cases, a wave packet and an incoherent superposition of plane waves give rise to the same shape of the interference pattern, provided that the intensity of the plane waves composing the incoherent superposition are equal to the square modulus of the amplitude of each Fourier component of the wave packet.