Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of the National Academy of Sciences

Remarks on the Quantum Theory of Diffraction

P. Ehrenfest, Paul Sophus Epstein

Published Jun 1, 1927• 51 citations
Publisher

Abstract

Before attacking the Fresnel problems we shall restate some of the considerations of our last paper, dealing with the Fraunhofer diffraction in a new form suitable for generalization [2]. The main question discussed in that paper was as to the intensity of light diffracted by any optical structure at a given angle to the incident beam. We saw there that the "electronic intensity," ρ of the diffracting system is a function of the space which may be referred to any system of coordinates. Let us use a rectangular cartesian system x, y, z and denote the cosines of the angles between the axes and the direction of the incident ray by αo, βo, γo.

DOI
10.1073/pnas.13.6.400

Related papers

Fresnel diffraction is a basic quantum mechanical effect

Mohammad Taghi Tavassoly

Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.

Journal of the Optical Society of America B•May 14, 2021•8 citations

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

B. Fabbro

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.

•Oct 26, 2017•3 citations

The Quantum Theory of the Fraunhofer Diffraction

Paul Sophus Epstein, P. Ehrenfest

In an important paper published on the pages of these PROCEEDINGS, W. Duane(1) makes a successful "attempt to formulate a theory of the reflection of X-rays by crystals, based on quantum ideas without reference to interference laws." A. H. Compton,(2) enlarging upon a hint contained in Duane's paper, has recently pointed out that the latter's hypothesis can be justified by the application of the general rules of the theory of quanta to the translatory motions of a crystal lattice.

Proceedings of the National Academy of Sciences•Apr 1, 1924•63 citations

Quantum Theory of Diffraction of Light

Deng Xiao-jiu

A general diffraction formula for plane apertures is derived by quantum theory and the results are in keeping with the present diffraction theories that attained by other methods. The viewpoint of photon diffraction can help us understand the nature of light diffraction and the evanescent waves is necessary for the uncertainty principle.[WT5”HZ]

Acta Sinica Quantum Optica•Jan 1, 2001•0 citations

Quantum Theory of Diffraction by an Aperture

B. Fabbro

A theoretical model of diffraction based on quantum mechanics is presented. It provides a general expression of the quantum state of a particle after its passage through an aperture in an opaque plane (diaphragm). In this model, the diaphragm is considered as a measurement device not only of the transverse coordinates but also of the longitudinal coordinate of the particle. Moreover, the change of state from the initial state (incident wave) to the final state (diffracted wave) results from two successive projections involving a transitional state which corresponds to the state of the particle when it is localized inside the aperture. These features of the model results from the need to ensure compatibility with the Huygens-Fresnel principle and with the kinematics constraints of the particle-diaphragm interaction. In the case of the diffraction at infinity (Fraunhofer diffraction), the predictions of the quantum model and of the classical theories based on the integrals of Fresnel-Kirchhoff (FK) and Rayleigh-Sommerfeld (RS1 and RS2) are different. They are close at small diffraction angles but contradictory at large angles. In this latter region, only the quantum and RS1 models predict the probable decrease in the intensity of the diffracted wave to zero when the diffraction angle reaches 90{\deg}. However, this decrease is different according to the model and it turns out that the discrepancies become significant beyond 60{\deg}. A measurement of the intensity of the particle flow in this region should allow to test the two theories.

•Oct 26, 2017•2 citations

Chapter 14 Dynamical diffraction of quantum beams: basic principles

Emil Zolotoyabko

De Gruyter eBooks•Jun 5, 2023•0 citations
Before attacking the Fresnel problems we shall restate some of the considerations of our last paper, dealing with the Fraunhofer diffraction in a new form suitable for generalization [2]. The main question discussed in that paper was as to the intensity of light diffracted by any optical structure at a given angle to the incident beam. We saw there that the "electronic intensity," ρ of the diffracting system is a function of the space which may be referred to any system of coordinates. Let us use a rectangular cartesian system x, y, z and denote the cosines of the angles between the axes and the direction of the incident ray by αo, βo, γo.
Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.
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.
In an important paper published on the pages of these PROCEEDINGS, W. Duane(1) makes a successful "attempt to formulate a theory of the reflection of X-rays by crystals, based on quantum ideas without reference to interference laws." A. H. Compton,(2) enlarging upon a hint contained in Duane's paper, has recently pointed out that the latter's hypothesis can be justified by the application of the general rules of the theory of quanta to the translatory motions of a crystal lattice.
A theoretical model of diffraction based on quantum mechanics is presented. It provides a general expression of the quantum state of a particle after its passage through an aperture in an opaque plane (diaphragm). In this model, the diaphragm is considered as a measurement device not only of the transverse coordinates but also of the longitudinal coordinate of the particle. Moreover, the change of state from the initial state (incident wave) to the final state (diffracted wave) results from two successive projections involving a transitional state which corresponds to the state of the particle when it is localized inside the aperture. These features of the model results from the need to ensure compatibility with the Huygens-Fresnel principle and with the kinematics constraints of the particle-diaphragm interaction. In the case of the diffraction at infinity (Fraunhofer diffraction), the predictions of the quantum model and of the classical theories based on the integrals of Fresnel-Kirchhoff (FK) and Rayleigh-Sommerfeld (RS1 and RS2) are different. They are close at small diffraction angles but contradictory at large angles. In this latter region, only the quantum and RS1 models predict the probable decrease in the intensity of the diffracted wave to zero when the diffraction angle reaches 90{\deg}. However, this decrease is different according to the model and it turns out that the discrepancies become significant beyond 60{\deg}. A measurement of the intensity of the particle flow in this region should allow to test the two theories.