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The Green's Function Method for Quantum Corrections to the Thomas-Fermi Model of the Atom (Classic Reprint) - Tapa blanda
Sinopsis
Uncover how Green's functions bridge many-body theory and the Thomas-Fermi model, starting from Hartree-Fock and moving to corrections that include exchange and inhomogeneity.
This work presents a systematic derivation that starts from the quantum many-body equations and shows how the Thomas-Fermi density appears as the leading term. It uses the Green's function formalism to connect ground-state properties with a practical, mixed position-momentum representation, and it discusses how higher-order corrections can be generated and interpreted. The discussion keeps the focus on core ideas while outlining how correlation effects might be included in future extensions.
- See how the Hartree-Fock approximation arises from the antisymmetric product of one-particle Green's functions.
- Learn how the zeroth-order term yields the Thomas-Fermi density and how the density is recovered from Green's functions.
- Understand how exchange and inhomogeneity effects appear together in the first non-vanishing correction to the Thomas-Fermi model.
- Explore the role of the mixed representation and the infinite-order differential operator that connects the Green's function to the original equations.
Ideal for readers of quantum many-body theory, atomic structure, and theoretical physics who want a clear path from a foundational model to its quantum corrections.
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Reseña del editor
Excerpt from The Green's Function Method for Quantum Corrections to the Thomas-Fermi Model of the Atom
The thomas-fermi model of the atom developed historically from reasonable physical assumptions about the nature of an atomic system. Because, however, the development was not a systematic derivation from the many body schrsdinger equation, it was difficult to incorporate corrections for certain higher order effects. Thus.
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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 The Green's Function Method for Quantum Corrections to the Thomas-Fermi Model of the Atom
A systematic method is presented for deriving the Thomas-Fermi equation for an atom and the quantum corrections from the many body description. The novel feature of the method is that it does not require any a priori assumptions about the distribution of the electrons in phase space but shows instead that the distribution which is usually assumed is a direct consequence of specifying that the many particle system is in its ground state. The procedure used in the derivation is the expansion of the mixed position-momentum representation of the Green's function in a series of powers of h. The lowest order term is found to correspond with the Thomas-Fermi density. The form of the higher order terms, which are to be considered as corrections to zeroth order term, depends on the approximations made in the many body equations for obtaining the Green's function. This paper deals only with the Hartree-Fock approximation, but the methods presented here allow generalization to other approximations which can include correlation effects.
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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The Green's Function Method for Quantum Corrections to the Thomas-Fermi Model
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Paperback. Condición: New. Print on Demand. This book provides a systematic method for solving the Thomas-Fermi model of the atom. The Thomas-Fermi model is a well-known approximation method used in quantum mechanics to describe the electronic structure of atoms. It is based on the assumption that the electrons in an atom move independently of each other in a self-consistent field. This book derives the Thomas-Fermi model from the many-body description of the atom, which takes into account the interactions between the electrons. The author shows that the Thomas-Fermi model is a good approximation for atoms with a large number of electrons. The book also discusses the quantum corrections to the Thomas-Fermi model, which are necessary to account for the effects of electron correlation. 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: 9781332133420_0
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The Green's Function Method for Quantum Corrections to the ThomasFermi Model of the Atom Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332133420
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The Green's Function Method for Quantum Corrections to the ThomasFermi Model of the Atom Classic Reprint
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332133420
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The Green's Function Method for Quantum Corrections to the Thomas-Fermi Model of the Atom (Classic Reprint)
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Forgotten Books, 2015
ISBN 10: 1332133428
ISBN 13: 9781332133420
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Condición: Hervorragend. Zustand: Hervorragend | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar. Nº de ref. del artículo: 26058086/1
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