On the quantum theory of diffraction by an aperture and the Fraunhofer diffraction at large angles

Abstract

A theoretical model of diffraction based on the concept of quantum measurement is presented. It provides a general expression of the state vector of a particle after its passage through an aperture of any shape in a plane screen (diaphragm). This model meets the double requirement of compatibility with the Huygens-Fresnel principle and with the kinematics of the particle-diaphragm interaction. This led to assume that the diaphragm is a device for measuring the three spatial coordinates of the particle and that the transition from the initial state (incident wave) to the final state (diffracted wave) consists of two specific projections which occur successively in a sequence involving a transitional state. In the case of the diffraction at infinity (Fraunhofer diffraction), the model predicts the intensity of the diffracted wave over the whole angular range of diffraction (0 • -90 • ). The predictions of the quantum model and of the theories of Fresnel-Kirchhoff (FK) and Rayleigh-Sommerfeld (RS1 and RS2) are close at small diffraction angles but significantly different at large angles, a region for which specific experimental studies are lacking. A measurement of the particle flow intensity in this region should make it possible to test the FK and RS1-2 theories and the suggested quantum model.

Rayleigh-Sommerfeld scalar diffraction by apertures moving at relativistic speeds

“…This is possible if the wavelength associated with an electron in the beam is much smaller than the dimension of the aperture. Otherwise, we need to generalize both the path-integral formalism of the quantum theory of diffraction for the Dirac spinors [13] and the quantum theory of diffraction in the light of quantum measurement [14] for the uniform motion of the apertures. We are also keeping this as an open problem.…”

Position measurement-induced collapse states: Proposal of an experiment

“…The question whether single-slit diffraction can be treated as quantum measurement of position of a particle was raised by Marcella [4] and was followed up in [5,6]. In a recent paper, we have obtained a satisfactory, affirmative answer [7] to the above question using the standard axioms of quantum mechanics, together with nonlocal quantum trajectory representations.…”

Position Measurement-Induced Collapse: A Unified Quantum Description of Fraunhofer and Fresnel Diffractions

“…This observation is based mainly on the fact that such treatises directly use the classical wave optics itself, instead of making a quantum mechanical approach, to explain diffraction, interference etc. This fundamental issue is addressed in some recent works [3,4,5], and the authors have proceeded further to explore the possibility that the diffraction through a single slit can be regarded as a prototype experiment to all position measurements. That is, they considered the slit in the diaphragm as a device for measuring the position of the incident particle, hoping that such an analysis shall be helpful for a general understanding of the quantum theory of position measurement.…”

“…Rothman and Boughn [4] have shown that this procedure in [3] is not compatible with standard quantum mechanics. Recently, Fabbro [5] has come up with an extension of the formalism in [3], in an attempt to rectify its drawbacks. Here it is inferred that these drawbacks come from the way in which the wave function reduction has been applied in it.…”

“…Here it is inferred that these drawbacks come from the way in which the wave function reduction has been applied in it. The model in [5] claims to predict the intensity of diffracted wave at large angles, focusing on the case of diffraction at infinity (Fraunhofer diffraction) only.…”