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). 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 based on the Huygens-Fresnel principle (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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Bernard Fabbro. On the quantum theory of diffraction by an aperture and the Fraunhofer diffraction at large angles. 2018. ⟨cea-01823747v1⟩

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