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Fermi–Dirac Statistics

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199646944
eISBN:
9780191775123
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646944.003.0028
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines the consequences of Fermi-Dirac statistics. The Fermi function is described, and the Fermi energy is found as the low-temperature limit of the chemical potential. The Sommerfeld ... More


Fermi–Dirac Statistics

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.003.0029
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

The main application of Fermi–Dirac Statistics is to calculate the properties of electrons. This chapter explains how the properties of fermions account for the behavior of metals. The Fermi energy ... More


Insulators and Semiconductors

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199646944
eISBN:
9780191775123
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646944.003.0029
Subject:
Physics, Condensed Matter Physics / Materials

Electrons in a crystal provide the most important example of a Fermi-Dirac system in a periodic potential. Due to Bloch's theorem, gaps occur in the density of states in such systems. When the Fermi ... More


Electrons in solids

Ian R. Kenyon

in Quantum 20/20: Fundamentals, Entanglement, Gauge Fields, Condensates and Topology

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198808350
eISBN:
9780191846052
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198808350.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

Electron energy bands in solids are introduced. Free electron theory for metals is presented: the Fermi gas, Fermi energy and temperature. Electrical and thermal conductivity are interpreted, ... More


Insulators and Semiconductors

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.003.0030
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

The origin of the strange band gaps that arise in the electron density of states in real materials is that the regular arrangement of the nuclei in a crystal lattice creates a periodic potential. ... More


Band Structure Theory for Extended Systems

Jochen Autschbach

in Quantum Theory for Chemical Applications: From Basic Concepts to Advanced Topics

Published in print:
2020
Published Online:
February 2021
ISBN:
9780190920807
eISBN:
9780197508350
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190920807.003.0013
Subject:
Chemistry, Quantum and Theoretical Chemistry

The electronic structure of infinite periodic systems (crystals) is treated with band structure theory, replacing molecular orbitals by crystal orbitals. The chapter starts out by introducing the ... More


Atoms, Molecules, Crystals and Semiconductor Devices

E. L. Wolf

in Physics and Technology of Sustainable Energy

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198769804
eISBN:
9780191822636
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198769804.003.0005
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

Properties of matter and of electronic devices are described, starting with Bohr’s model of the hydrogen atom. Motion of electrons in a periodic potential is shown to allow energy ranges with free ... More


Quantum Mechanical Ensemble Averages and Statistical Thermodynamics

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble ... More


Bosons and Fermions: Indistinguishable Particles with Intrinsic Spin

Duncan G. Steel

in Introduction to Quantum Nanotechnology: A Problem Focused Approach

Published in print:
2021
Published Online:
July 2021
ISBN:
9780192895073
eISBN:
9780191924149
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895073.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

If we imagine a Hamiltonian, H^(r1,r2), describing two identical particles at positions r1 and r2 and then we interchange the particles, the Hamiltonian will be unaffected, i.e. H^(r1,r2)=H^(r2,r1). ... More


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