Quantum Theory of Neutron Diffraction

Wu, Xiaofeng; Zhang, Baijun; Liu, Xiaojing; Liu, Bing; Zhang, Chunli; Li, Jing-Wu

doi:10.1142/s0217979209052601

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…Contrary to (15), the equation ( 18) makes sense at the limit ∆z = 0, provided that F 0 L (z) = C(z) δ(z) where C(z) is any function of arbitrary dimension. Indeed, in this case ( 18) implies: lim ∆z→0 z ψ ∆z z 2 = δ(z), whatever C(z). The easiest way is to choose C(z) = 1, dimensionless so that F 0 L (z) = δ(z) and therefore is positive and normalized to 1.…”

Section: B Projection Of the Initial State Position Filteringmentioning

confidence: 96%

“…Then, models involving quantum mechanics to calculate diffraction are mostly those based on the formalism of path integrals [11][12][13][14] and those predicting quantum trajectories in the framework of hidden variables theories [15][16][17]. Other models combine the resolution of the Schrödinger equation (or of the wave equation for photons) with the Huygens-Fresnel principle [18][19][20]. Only one calculation based explicitly on the concept of quantum measurement -therefore involving state vectors in a Hilbert spaceseems to have been done until now.…”

Section: Introductionmentioning

confidence: 99%

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

Fabbro¹

2017

Preprint

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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.

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Section: B Projection Of the Initial State Position Filteringmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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

Fabbro¹

2017

Preprint

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“…1a. i) The principal maximum corresponds to the mean value of the momentum 0 >= < y k given by the set of functions ) ( y n k Q in (2). ii) The secondary maxima appear for the wave vectors corresponding to the eigenstates in the equation (1).…”

mentioning

confidence: 99%

A Quantum Mechanics Treatment of Electron Diffraction by a Slit

Lovey

2020

Microsc Microanal

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The diffraction of particles (electrons, neutrons, protons, atoms) by slits is a phenomenon that should be treated in the frame of quantum mechanics (QM) by solving the Schrodinger equation. However in most cases the Huygens principle and/or the Kirchhoff and Fresnel formalisms have been used. An approach to apply QM to the diffraction of particles by a single or double slit was reported in reference [1]. However they proposal can only be applied when the opaque plate containing the slits has a negligible thickness. More recently in another report [2] the diffraction of neutrons by slits was analyzed. These authors considered the slit as an infinite potential well. The particles when traversing the slit must occupy the quantum states due to this well potential. Nevertheless, the authors fail giving a complete QM description as they applied the classic Kirchhoff formulation at the exit plane of the slit.

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Spatial and temporal description of electron diffraction through a double slit at the nanometer scale

Castellanos-Jaramillo

Castellanos-Moreno

2018

Eur. J. Phys.

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The goal of this paper is to study double-slit diffraction at the nanometric scale. We treat the time evolution of a Gaussian wave packet in quantum mechanics traveling until it reaches a double-slit wall. A detailed investigation and analysis of the diffraction phenomenon and its progress is developed by numerically solving the Schrödinger equation. This is written using a potential intended to model the wall. It is solved by using finite differences in the time domain method, so that the probability amplitude, ψ, is obtained as a function of the spatial coordinates at discretized times. Then, the probability density, ρ, is found in a straightforward way and used to plot graphics or make videos. Furthermore, the time evolution of the wave packet is registered at several fixed points to acquire local information. Fourier transforms are calculated to complement the knowledge obtained. Students interested in didactic approaches, or in applications for nanodevices, could find interest in this approach.

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Quantum Theory of Neutron Diffraction

Cited by 3 publications

References 7 publications

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

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

A Quantum Mechanics Treatment of Electron Diffraction by a Slit

Spatial and temporal description of electron diffraction through a double slit at the nanometer scale

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