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

The Quantum Theory of the Fraunhofer Diffraction

Paul Sophus Epstein, P. Ehrenfest

Published Apr 1, 1924• 63 citations
Publisher

Abstract

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.

DOI
10.1073/pnas.10.4.133

Related papers

Remarks on the Quantum Theory of Diffraction

P. Ehrenfest, Paul Sophus Epstein

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.

Proceedings of the National Academy of Sciences•Jun 1, 1927•51 citations

Some Applications and Implications of Duane's Quantum Theory of Diffraction

Evan James Williams

Duane's quantum theory of diffraction is applied to the reflexion of electrons by crystals and to the spatial distribution of photoelectrons and fluorescent radiation from a crystal. Two alternative criteria for coherence are given. According to the second of these there is coherence provided that the momentum imparted to the components of a system during the process concerned is insufficient, owing to quantum restrictions to their motion, to change their energy. Calculations made on this supposition show that in the case of the scattering of radiation by a crystal there is complete coherence for the lower orders, while for higher orders this ceases to be the case and the reflected intensity is reduced as the result of incoherent scattering. The specular reflexion by gases is also considered. Duane's theory of diffraction has not been placed on a rigorous basis and the solutions which have been proposed here for various problems may be incorrect. Even so the theory has at least served to bring to light several points of theoretical and experimental interest which deserve consideration.

Mathematical Proceedings of the Cambridge Philosophical Society•Apr 1, 1928•3 citations

The nature of light: a description of photon diffraction based upon virtual particle exchange

Michael J. Mobley

Any discussion of the nature of light must include a reminder that whenever we make the observation of light (photons), we only observe particle-like properties. This paper provides a reiteration that we don't need wave-like properties to scattered photons to describe phenomena such as diffraction or refraction of light. This paper updates the original ideas of Duane, later revived by Lande, which provided a description of light diffraction without making reference to a wave nature. These are updated using terminology more common to quantum electrodynamics which describes the interaction of particles in terms of the exchange of virtual photons. Diffraction is described in terms of an ensemble of distinct, probability weighted paths for the scattered photons. The scattering associated with each path results from the quantized momentum exchange with the scattering lattice attributed to the exchange or reflection of virtual photons. The probability for virtual particle exchange/reflection is dependent upon the allowed momentum states of the lattice determined by a Fourier analysis of the lattice geometry. Any scattered photon will exhibit an apparent wavelength inversely proportional to its momentum. Simplified, particle-like descriptions are developed for Young's double slit diffraction, Fraunhofer diffraction and Fresnel diffraction. This description directly accounts for the quantization of momentum transferred to the scattering lattice and the specific eigenvalues of the lattice based upon the constraints to virtual photon exchange set by the Uncertainty Principle, Δπi = h/ζi.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 1, 2005•5 citations

Note on the Quantum Theory of the Reflection of X-Rays

William C. Duane

Proceedings of the National Academy of Sciences•Mar 1, 1925•3 citations

Uncertainty and Complementarity

Kurt Gottfried

The creation of quantum mechanics in the period 1924–1928 restored logical consistency to its rightful place in theoretical physics. The study of interaction between light and electrons provided most of the important clues in the development of the quantum theory. This chapter shows that in the interference experiments the statistical distribution of quanta is correctly given by the intensity of the wave field as computed from classical electromagnetic theory. It also shows that under special circumstances the classical theory also makes contact with some of the empirical facts in Compton's experiment. The chapter discusses a famous example due to W. Heisenberg, in which Compton scattered γ-rays are brought to focus by a microscope. It provides the uncertainty relations for the dynamical variables of a particle from the conservation laws and the properties of photons. Because the motion of charged particles can be deduced from their attendant fields, it is clear that fields cannot be measured to arbitrary precision.

CRC Press eBooks•Mar 9, 2018•2 citations

Quantum theory of X-ray reflection: Mathematical formulation

Chandrasekhara Venkata Raman

Proceedings of the Indian Academy of Sciences - Section A•Oct 1, 1941•2 citations
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.
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.
Duane's quantum theory of diffraction is applied to the reflexion of electrons by crystals and to the spatial distribution of photoelectrons and fluorescent radiation from a crystal. Two alternative criteria for coherence are given. According to the second of these there is coherence provided that the momentum imparted to the components of a system during the process concerned is insufficient, owing to quantum restrictions to their motion, to change their energy. Calculations made on this supposition show that in the case of the scattering of radiation by a crystal there is complete coherence for the lower orders, while for higher orders this ceases to be the case and the reflected intensity is reduced as the result of incoherent scattering. The specular reflexion by gases is also considered. Duane's theory of diffraction has not been placed on a rigorous basis and the solutions which have been proposed here for various problems may be incorrect. Even so the theory has at least served to bring to light several points of theoretical and experimental interest which deserve consideration.
Any discussion of the nature of light must include a reminder that whenever we make the observation of light (photons), we only observe particle-like properties. This paper provides a reiteration that we don't need wave-like properties to scattered photons to describe phenomena such as diffraction or refraction of light. This paper updates the original ideas of Duane, later revived by Lande, which provided a description of light diffraction without making reference to a wave nature. These are updated using terminology more common to quantum electrodynamics which describes the interaction of particles in terms of the exchange of virtual photons. Diffraction is described in terms of an ensemble of distinct, probability weighted paths for the scattered photons. The scattering associated with each path results from the quantized momentum exchange with the scattering lattice attributed to the exchange or reflection of virtual photons. The probability for virtual particle exchange/reflection is dependent upon the allowed momentum states of the lattice determined by a Fourier analysis of the lattice geometry. Any scattered photon will exhibit an apparent wavelength inversely proportional to its momentum. Simplified, particle-like descriptions are developed for Young's double slit diffraction, Fraunhofer diffraction and Fresnel diffraction. This description directly accounts for the quantization of momentum transferred to the scattering lattice and the specific eigenvalues of the lattice based upon the constraints to virtual photon exchange set by the Uncertainty Principle, Δπi = h/ζi.
The creation of quantum mechanics in the period 1924–1928 restored logical consistency to its rightful place in theoretical physics. The study of interaction between light and electrons provided most of the important clues in the development of the quantum theory. This chapter shows that in the interference experiments the statistical distribution of quanta is correctly given by the intensity of the wave field as computed from classical electromagnetic theory. It also shows that under special circumstances the classical theory also makes contact with some of the empirical facts in Compton's experiment. The chapter discusses a famous example due to W. Heisenberg, in which Compton scattered γ-rays are brought to focus by a microscope. It provides the uncertainty relations for the dynamical variables of a particle from the conservation laws and the properties of photons. Because the motion of charged particles can be deduced from their attendant fields, it is clear that fields cannot be measured to arbitrary precision.