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Proceedings of the Indian Academy of Sciences - Section A

The quantum theory of X-ray reflection: Basic ideas

Chandrasekhara Venkata Raman

Published Oct 1, 1941• 8 citations
Publisher
DOI
10.1007/bf03046075

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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.

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Starting from the time-independent Schrodinger equation for elastic scattering a theory of wave-particle duality is developed which takes into account effects due to the quantum potential by means of a generalised ray equation. The duality between waves and particles is expressed in terms of two basic equations. Wave effects are described by a nonlinear amplitude equation which is coupled to a generalized ray equation that describes particle effects. The coupling between these two aspects of duality occurs by means of a function called the quantum expansion coefficient which describes the way in which a bundle of ray paths expand as the propagation distance increases. For systems in which the phase of the one-body wavefunction is a separable function of its coordinates, the authors derive simplified forms for the ray equations. As an example the authors show how the theory may be used to calculate tunnelling ray paths in planar electron channelling. The reflected rays in this case originate from beyond the classical turning points, thereby demonstrating the existence of a Goos-Hanchen effect in electron channeling.

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Basic Concepts & Formulation

Nandita Rudra

Newtonian Mechanics, theory of Elasticity and Fluid Dynamics, together with Maxwellian Newtonian Mechanics, theory of Elasticity and Fluid Dynamics, together with Maxwellian Electrodynamics are basically what constitute Classical Physics. Classical Physics was developed and successfully applied to describe the motions of macroscopic bodies like planetary systems and other every day phenomena. It also described electromagnetic field and its interaction with matter. The development of classical physics was almost complete by the early twentieth century. With the discovery of subatomic particles, radioactivity and X-rays and also the accumulation of data on the spectrum of Black Body Radiation and other spectroscopic studies, it became imperative to invoke new concepts and ideas. Thus Quantum Mechanics, the fundamental theory of the physical world was formulated.

CRC Press eBooks•Aug 19, 2019•0 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.
Starting from the time-independent Schrodinger equation for elastic scattering a theory of wave-particle duality is developed which takes into account effects due to the quantum potential by means of a generalised ray equation. The duality between waves and particles is expressed in terms of two basic equations. Wave effects are described by a nonlinear amplitude equation which is coupled to a generalized ray equation that describes particle effects. The coupling between these two aspects of duality occurs by means of a function called the quantum expansion coefficient which describes the way in which a bundle of ray paths expand as the propagation distance increases. For systems in which the phase of the one-body wavefunction is a separable function of its coordinates, the authors derive simplified forms for the ray equations. As an example the authors show how the theory may be used to calculate tunnelling ray paths in planar electron channelling. The reflected rays in this case originate from beyond the classical turning points, thereby demonstrating the existence of a Goos-Hanchen effect in electron channeling.
Newtonian Mechanics, theory of Elasticity and Fluid Dynamics, together with Maxwellian Newtonian Mechanics, theory of Elasticity and Fluid Dynamics, together with Maxwellian Electrodynamics are basically what constitute Classical Physics. Classical Physics was developed and successfully applied to describe the motions of macroscopic bodies like planetary systems and other every day phenomena. It also described electromagnetic field and its interaction with matter. The development of classical physics was almost complete by the early twentieth century. With the discovery of subatomic particles, radioactivity and X-rays and also the accumulation of data on the spectrum of Black Body Radiation and other spectroscopic studies, it became imperative to invoke new concepts and ideas. Thus Quantum Mechanics, the fundamental theory of the physical world was formulated.