## The Hartree–Fock approximation

*Helmut Hofmann*

### in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0020
- Subject:
- Physics, Nuclear and Plasma Physics

This chapter formulates the Hartree-Fock approximation with density matrices, and discusses the properties of the Hartree-Fock equations together with the energy functional for the ground state ... More

## Classical Ensembles: Grand and Otherwise

*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/9780199646944.003.0020
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter introduces the grand canonical ensemble and demonstrates how to calculate the grand canonical partition function for a classical ideal gas. One purpose of the introduction of the grand ... More

## Basic principles

*Barry M. McCoy*

### in Advanced Statistical Mechanics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the basic results of thermodynamics. It derives the basic formulas of the canonical and grand canonical ensemble from the microcanonical ensemble. It defines the concept of a ... More

## Equilibrium Statistical Mechanics

*Hans-Peter Eckle*

### in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Chapter 4 reviews the basic notions of equilibrium statistical mechanics and begins with its fundamental postulate and outlines the structure of the theory using the most important of the various ... More

## The chemical potential

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0006
- Subject:
- Chemistry, Theoretical Chemistry

In this chapter, the concepts and form of elementary quantum mechanics are generalized. This allows use of variables other than coordinates for the description of a state, permits ready discussion ... More

## Density-functional theory

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0005
- Subject:
- Chemistry, Theoretical Chemistry

In this chapter, the concepts and form of elementary quantum mechanics are generalized. This allows use of variables other than coordinates for the description of a state, permits ready discussion ... More

## Review Of Some Mathematical And Physical Subjects

*Abraham Nitzan*

### in Title Pages

- Published in print:
- 2006
- Published Online:
- November 2020
- ISBN:
- 9780198529798
- eISBN:
- 9780191916649
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198529798.003.0006
- Subject:
- Chemistry, Physical Chemistry

This chapter reviews some subjects in mathematics and physics that are used in different contexts throughout this book. The selection of subjects and the level of their coverage reflect the ... More

## Quantum Canonical Ensemble

*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/9780199646944.003.0023
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter derives the canonical ensemble, which is arguably the most important concept in quantum statistical mechanics. The associated partition function leads to a quantum statistical mechanics ... More

## The Ideal Bose Gas

*Lev Pitaevskii and Sandro Stringari*

### in Bose-Einstein Condensation and Superfluidity

- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780198758884
- eISBN:
- 9780191818721
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198758884.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter describes the mechanism of Bose–Einstein condensation in the simplest ideal Bose gas case. An explicit expression for the critical temperature is derived in the analytically soluble case ... More

## Quantum Canonical Ensemble

*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/9780198853237.003.0024
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This chapter introduces the quantum mechanical canonical ensemble, which is used for the majority of problems in quantum statistical mechanics. The ensemble is derived and analogies with the ... More

## Density matrices

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0004
- Subject:
- Chemistry, Theoretical Chemistry

In this chapter, the concepts and form of elementary quantum mechanics are generalized. This allows use of variables other than coordinates for the description of a state, permits ready discussion ... 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

## Thermodynamic Green’s Functions and Spectral Structure

*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/9780198791942.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the ... More

## Introduction

*C. G. Gray and K. E. Gubbins*

### in

- Published in print:
- 1984
- Published Online:
- November 2020
- ISBN:
- 9780198556022
- eISBN:
- 9780191919251
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198556022.003.0007
- Subject:
- Chemistry, Theoretical Chemistry

The application of statistical mechanics to the study of fluids over the past fifty years † or so has progressed through a series of problems of gradually increasing difficulty. The first and most ... More

## Extensions

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0011
- Subject:
- Chemistry, Theoretical Chemistry

## Chemical potential derivatives

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0007
- Subject:
- Chemistry, Theoretical Chemistry

## Elementary wave mechanics

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0003
- Subject:
- Chemistry, Theoretical Chemistry

## The Kohn–Sham method: Basic principles

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0009
- Subject:
- Chemistry, Theoretical Chemistry

## The Kohn-Sham method: Elaboration

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0010
- Subject:
- Chemistry, Theoretical Chemistry

## Aspects of atoms and molecules

*Robert G. Parr and Yang Weitao*

### in Density-Functional Theory of Atoms and Molecules

- Published in print:
- 1995
- Published Online:
- November 2020
- ISBN:
- 9780195092769
- eISBN:
- 9780197560709
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195092769.003.0012
- Subject:
- Chemistry, Theoretical Chemistry