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A Hartree Self Consistent Method for the Scattering of Positrons by Hydrogen Atoms (Classic Reprint) - Tapa blanda
Sinopsis
Excerpt from A Hartree Self Consistent Method for the Scattering of Positrons by Hydrogen Atoms
Our aim has been to develop a method whereby the self - consistent features of the Hartree approach can be incorporated into a form.for the wave function which will contain correlations and satisfy the asymptotic boundary conditions. We have accomplished this by adding a sum of products of one particle functions to a product of the unperturbed bound state wave function and a function which will have the proper asymp totic form for a scattered particle. By requiring the terms in the sum to vanish at large distances, we have been able to obtain a set of coupled differential equations for the one particle functions. We can show that these differential equations lead to an effective one-particle Hamiltonian for the scattered particle in which the potential is made up of a sum of induced multipole potentials. We can also show that with a suitable set of approximations, the equations reduce to the adiabatic approximation.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Reseña del editor
Excerpt from A Hartree Self Consistent Method for the Scattering of Positrons by Hydrogen Atoms
Our aim has been to develop a method whereby the self - consistent features of the Hartree approach can be incorporated into a form.for the wave function which will contain correlations and satisfy the asymptotic boundary conditions. We have accomplished this by adding a sum of products of one particle functions to a product of the unperturbed bound state wave function and a function which will have the proper asymp totic form for a scattered particle. By requiring the terms in the sum to vanish at large distances, we have been able to obtain a set of coupled differential equations for the one particle functions. We can show that these differential equations lead to an effective one-particle Hamiltonian for the scattered particle in which the potential is made up of a sum of induced multipole potentials. We can also show that with a suitable set of approximations, the equations reduce to the adiabatic approximation.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from A Hartree Self Consistent Method for the Scattering of Positrons by Hydrogen Atoms
Refinements on the one product scheme have been proposed by and Temkin Seaton suggests that the total wave function be expanded as a series of terms consisting of solutions to the bound state problem with coefficients which depend on the coordinates of the scattered elec tron. However, since one can expect an infinite number of terms the series must be truncated in order to compute the coefficients. Having once computed the coefficients, there is no machinery for going back and improving the estimate of the bound state distortion. Temkin uses the adiabatic approximation to compute the distortion of the bound state. He assumes that the incident electron is moving so slowly that one can cousi der the atom to be in the field of a static charge. By means of pertur bation theory he is able to compute a distorted bound state wave function which depends parametrically on the position of the incident particle.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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A Hartree Self Consistent Method for the Scattering of Positrons by Hydrogen
Impresión bajo demandaLibrería: Forgotten Books, London, Reino Unido
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Paperback. Condición: New. Print on Demand. This book delves into the complexities of positron scattering, a fascinating phenomenon that occurs when positrons interact with hydrogen atoms. The author meticulously formulates a self-consistent method using a wave function that incorporates correlations and adheres to asymptotic boundary conditions. Through this innovative approach, the author unveils the intricate relationship between the scattering process and the induced multipole potential, providing a deeper understanding of the underlying dynamics. Notably, the author demonstrates that the approximation of the scattering process to the adiabatic approximation, a commonly used technique, is valid under certain conditions. This book offers a significant contribution to our understanding of positron scattering, showcasing the power of self-consistent methods in unraveling the complexities of atomic interactions. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781333041144_0
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A Hartree Self Consistent Method for the Scattering of Positrons by Hydrogen Atoms Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781333041144
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A Hartree Self Consistent Method for the Scattering of Positrons by Hydrogen Atoms Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781333041144
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