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An algebraic approach to the many-electron problem

Record Type:	Electronic resources : Monograph/item
Title/Author:	An algebraic approach to the many-electron problemby Jaroslav Zamastil, Tereza Uhlířová.
Author:	Zamastil, Jaroslav.
other author:	Uhlířová, Tereza.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	viii, 71 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Hartree-Fock approximation.
Online resource:	https://doi.org/10.1007/978-3-031-87825-1
ISBN:	9783031878251$q(electronic bk.)

An algebraic approach to the many-electron problem
Zamastil, Jaroslav.

An algebraic approach to the many-electron problem[electronic resource] /by Jaroslav Zamastil, Tereza Uhlířová. - Cham :Springer Nature Switzerland :2025. - viii, 71 p. :ill., digital ;24 cm. - SpringerBriefs in physics,2191-5431. - SpringerBriefs in physics..

Chapter 1: Quantized electron field -- Chapter 2: Hartree-Fock approximation -- Chapter 3: Coupled cluster method -- Chapter 4: Further developments.

This book presents an algebraic approach to the coupled cluster method for many-electron systems, pioneered by Josef Paldus. Using field methods along with an algebraic, rather than diagrammatic, approach facilitates a way of deriving the coupled cluster method which is readily understandable at the graduate level. The book begins with the notion of the quantized electron field and shows how the N-electron Hamiltonian can be expressed in its language. This is followed by introduction of the Fermi vacuum and derivation of the Hartree-Fock equations along with conditions for stability of their solutions. Following this groundwork, the book discusses a method of configuration interaction to account for dynamical correlations between electrons, pointing out the size-extensivity problem, and showing how this problem is solved with the coupled cluster approach. This is followed by derivation of the coupled cluster equations in spin-orbital form. Finally, the book explores practical aspects, showing how one may take advantage of permutational and spin symmetries, and how to solve coupled-cluster equations, illustrated by the Hubbard model of benzene, the simplest quasi-realistic model of electron correlation.

ISBN: 9783031878251$q(electronic bk.)

Standard No.: 10.1007/978-3-031-87825-1doiSubjects--Topical Terms:

233542
Hartree-Fock approximation.

LC Class. No.: QC176.8.E4

Dewey Class. No.: 530.144015114

An algebraic approach to the many-electron problem
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520 $a This book presents an algebraic approach to the coupled cluster method for many-electron systems, pioneered by Josef Paldus. Using field methods along with an algebraic, rather than diagrammatic, approach facilitates a way of deriving the coupled cluster method which is readily understandable at the graduate level. The book begins with the notion of the quantized electron field and shows how the N-electron Hamiltonian can be expressed in its language. This is followed by introduction of the Fermi vacuum and derivation of the Hartree-Fock equations along with conditions for stability of their solutions. Following this groundwork, the book discusses a method of configuration interaction to account for dynamical correlations between electrons, pointing out the size-extensivity problem, and showing how this problem is solved with the coupled cluster approach. This is followed by derivation of the coupled cluster equations in spin-orbital form. Finally, the book explores practical aspects, showing how one may take advantage of permutational and spin symmetries, and how to solve coupled-cluster equations, illustrated by the Hubbard model of benzene, the simplest quasi-realistic model of electron correlation.
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