Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T15:44:20.137Z Has data issue: false hasContentIssue false

13 - Many-Electron Systems

Published online by Cambridge University Press:  11 May 2023

Uri Peskin
Affiliation:
Technion - Israel Institute of Technology, Haifa
Get access

Summary

The foundations for understanding the electronic structure of many-electron atoms are introduced. We start from the discovery of the spin and introduce spin operators. The spin existence is shown to “upgrade” the state of single particles into a product space with the spin subspace, and to impose constraints on states of identical particles, which must be symmetric (bosons) or antisymmetric (fermions) under particle transpositions. The many-electron state in the atom is therefore approximated as an antisymmetrized products (Slater determinant) of single-electron states (spin-orbitals). The variationally optimal orbitals are shown to be solutions to the Hartree–Fock equations, and the assignment of electrons to these orbitals in the atomic ground state reflects the Pauli exclusion and Aufbau principles, thus explaining the trends in the periodic table of the elements in terms of their electronic configurations. Special attention is given to two-electron systems, demonstrating the exchange stabilization of triplet versus singlet states (Hund’s rule).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Zeeman, P., “The Effect of Magnetisation on the Nature of Light Emitted by a Substance”, Nature 55, 347 (1897).CrossRefGoogle Scholar
Gerlach, W. and Stem, O., “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld,” Zeitschrift für Physik 9, 349 (1922).CrossRefGoogle Scholar
Thaller, B., “The Dirac Equation” (Springer Science Berlin Heidelberg, 1992).Google Scholar
Jackson, J. D., “Classical Electrodynamics,” 3rd ed. (Wiley, 1999).Google Scholar
Slater, J. C., “The theory of complex spectra,” Phys. Rev. 34, 1293 (1929).Google Scholar
Fock, V., “Naherungsmethode zur Losung des quantenmechanischen Mehrkorperproblems,” Zeitschrift für Physik 61, 126 (1930).CrossRefGoogle Scholar
Szabo, A. and Ostlund, N. S., “Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory” (Dover, 1996).Google Scholar
Latter, R., “Atomic energy levels for the Thomas-Fermi and Thomas-Fermi-Dirac potential,” Physical Review 99, 510 (1955).Google Scholar
Parr, R. G. and Yang, W., “Density Functional Theory of Atoms and Molecules” (Oxford University Press, 1989).Google Scholar
Bartlett, R. J. and Musiał, M., “Coupled-cluster theory in quantum chemistry,” Reviews of Modern Physics 79, 291 (2007).CrossRefGoogle Scholar
Pauncz, R., “Spin Eigenfunctions: Construction and Use” (Springer, 1979).CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Many-Electron Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.014
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Many-Electron Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.014
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Many-Electron Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.014
Available formats
×