Bounds on Elements of the S Matrix for Elastic Scattering: One Dimensional Scattering (Classic Reprint) - Softcover
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Excerpt from Bounds on Elements of the S Matrix for Elastic Scattering: One Dimensional Scattering
In this paper, we will consider multi-channel scattering in which the scattering matrix cannot be diagonalized a priori. More formally.
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Excerpt from Bounds on Elements of the S Matrix for Elastic Scattering: One Dimensional Scattering
In this paper, we will consider multi-channel scattering in which the scattering matrix cannot be diagonalized a priori. More formally.
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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Excerpt from Bounds on Elements of the S Matrix for Elastic Scattering: One Dimensional Scattering
Kato has demonstrated the possibility of determining upper and lover bounds on cot x, where q is the phase shift for arbitrary angular monentum. for the quantum mechanical scattering of a particle by a static central potential. The basic interest of the method derives; from the fact that the expression for either bound includes a variational trial function, and gives an error which is of second order in the difference between the trial function and the exact function. The bounds are therefore also variational estimates, and might be termed variational bounds. In subsequent studies, 2, 3, 4, the case of angular moments greater than zero was considered more intensively, some slight extensions and improvements in the formalism were effected, and some pre-liminary results were obtained for the applicability of the method to scattering by compound systems with emphasis on the low energy scattering of positrons by Hydrogen atoms.
Static central potential scattering problems involve an infinite number of channels which are however uncoupled, a consequence of conservation of angular momentus. In other words, an expansion into partial waves leads to a diagonalization of the scattering matrix S before the detailed analysis is begun. Furthermore, each angular momentum channel wave function is completely characterised by one real number, the real phase shift for that angular momentun.
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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Bounds on Elements of the S Matrix for Elastic Scattering (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book is an investigation into the development of variational bounds on scattering phenomena. The author demonstrates a new approach to the problem of determining upper and lower bounds on the elements of multichannel scattering matrices. The method is applicable whenever the scattering matrix can be diagonalized on some a priori basis, and involves the introduction of an integral variational principle which is cast as an identity. While the variational principle itself is not a new concept, the present approach shows how to bound the explicitly exhibited second order term. Numerical examples are calculated for a one-dimensional attractive square well asymmetric with respect to the origin. The author's work is significant because the method presented here can provide useful results in many multi-channel problems for which there would otherwise be no practical approach. 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. Bestandsnummer des Verkäufers 9781332106196_0
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Bounds on Elements of the S Matrix for Elastic Scattering One Dimensional Scattering Classic Reprint
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Bounds on Elements of the S Matrix for Elastic Scattering One Dimensional Scattering Classic Reprint
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