An Algebraic Approach to the Many-Electron Problem
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...
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| Médium: | Elektronický zdroj E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
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Springer Nature Switzerland : Imprint: Springer,
2025.
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| Vydání: | 1st ed. 2025. |
| Edice: | SpringerBriefs in Physics,
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| Témata: | |
| On-line přístup: | https://doi.org/10.1007/978-3-031-87825-1 |
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| Shrnutí: | 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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| Fyzický popis: | 1 online resource (VIII, 71 p.). |
| ISBN: | 9783031878251 |
| ISSN: | 2191-5431 |
| DOI: | 10.1007/978-3-031-87825-1 |