On the quantum theory of diffraction by an aperture and the Fraunhofer diffraction at large angles. (arXiv:1710.09758v2 [quant-ph] UPDATED)

A quantum model of diffraction providing a general expression of the quantum
state of a particle after its passage through an aperture in a plane screen
(diaphragm) is presented. In this model, the diaphragm is considered as a
measurement device of the position of the particle and the postulate of wave
function reduction is applied to describe the change of state of the particle
during the measurement. It is shown that this change of state is more complex
than a single projection because of the kinematics of the particle-diaphragm
interaction. In the case of the diffraction at infinity (Fraunhofer
diffraction), the model makes it possible to predict the intensity of the
diffracted wave over the whole diffraction angle range (0 - 90 degrees). The
predictions of the quantum model and of the classical 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 intensity
of the particle flow in this region should allow to test the classical theories
and the presented quantum model.

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