An Algebraic Approach to the Many-Electron Problem

• Verfasst von: Zamastil, Jaroslav [VerfasserIn]
• Verfasst von: Uhlířová, Tereza [VerfasserIn]
• Titel: An Algebraic Approach to the Many-Electron Problem
• Verf.angabe: by Jaroslav Zamastil, Tereza Uhlířová
• Ausgabe: 1st ed. 2025.
• Verlagsort: Cham
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Verlag: Imprint: Springer
• E-Jahr: 2025
• Jahr: 2025.
• Jahr: 2025.
• Umfang: 1 Online-Ressource(VIII, 71 p.)
• Gesamttitel/Reihe: SpringerBriefs in Physics
• ISBN: 978-3-031-87825-1
• DOI: doi:10.1007/978-3-031-87825-1
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• K10plus-PPN: 1925485986
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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

Abstract

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.