Helmut Hofmann
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0026
- Subject:
- Physics, Nuclear and Plasma Physics
This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, ...
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This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, representations of the delta-function are given and applied to Fourier and Laplace transformations. For quantal operators, the Mori product is introduced and an important formula for the derivative of exponentials is shown. Elementary properties of spin and isospin are discussed; for fermions, the formalism of second quantization is produced.Less
This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, representations of the delta-function are given and applied to Fourier and Laplace transformations. For quantal operators, the Mori product is introduced and an important formula for the derivative of exponentials is shown. Elementary properties of spin and isospin are discussed; for fermions, the formalism of second quantization is produced.
Hans-Peter Eckle
- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials
Chapter 2 provides a review of pertinent aspects of the quantum mechanics of systems composed of many particles. It focuses on the foundations of quantum many-particle physics, the many-particle ...
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Chapter 2 provides a review of pertinent aspects of the quantum mechanics of systems composed of many particles. It focuses on the foundations of quantum many-particle physics, the many-particle Hilbert spaces to describe large assemblies of interacting systems composed of Bosons or Fermions, which lead to the versatile formalism of second quantization as a convenient and eminently practical language ubiquitous in the mathematical formulation of the theory of many-particle systems of quantum matter. The main objects in which the formalism of second quantization is expressed are the Bosonic or Fermionic creation and annihilation operators that become, in the position basis, the quantum field operators.Less
Chapter 2 provides a review of pertinent aspects of the quantum mechanics of systems composed of many particles. It focuses on the foundations of quantum many-particle physics, the many-particle Hilbert spaces to describe large assemblies of interacting systems composed of Bosons or Fermions, which lead to the versatile formalism of second quantization as a convenient and eminently practical language ubiquitous in the mathematical formulation of the theory of many-particle systems of quantum matter. The main objects in which the formalism of second quantization is expressed are the Bosonic or Fermionic creation and annihilation operators that become, in the position basis, the quantum field operators.
Xiao-Gang Wen
- Published in print:
- 2007
- Published Online:
- February 2010
- ISBN:
- 9780199227259
- eISBN:
- 9780191713019
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227259.003.03
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive ...
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This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive the superfuid phase, which results in a low energy effective non-linear sigma model. A renormalization group approach is introduced to study the zero temperature quantum phase transition between superfluid and Mott insulator phase, and finite temperature phase transition between superfluid and normal phase. The physics and the importance of symmetry breaking in phase transitions and in protecting gapless excitations are discussed. The phenomenon of superfluidity and superconductivity is also discussed, where the coupling to U(1) gauge field is introduced.Less
This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive the superfuid phase, which results in a low energy effective non-linear sigma model. A renormalization group approach is introduced to study the zero temperature quantum phase transition between superfluid and Mott insulator phase, and finite temperature phase transition between superfluid and normal phase. The physics and the importance of symmetry breaking in phase transitions and in protecting gapless excitations are discussed. The phenomenon of superfluidity and superconductivity is also discussed, where the coupling to U(1) gauge field is introduced.
Vladimir M. Agranovich
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199234417
- eISBN:
- 9780191715426
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234417.003.0015
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter describes the approximate second quantization and approximate transition to boson picture. Using exact transformation from paulions to bosons, the collective properties of an ideal ...
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This chapter describes the approximate second quantization and approximate transition to boson picture. Using exact transformation from paulions to bosons, the collective properties of an ideal three-dimensional gas of paulions are considered. The statistics and the collective properties of Frenkel excitons are discussed, taking into account the dynamic exciton-exciton interaction. The fermionic character of Frenkel excitons in one-dimensional molecular crystals is demonstrated.Less
This chapter describes the approximate second quantization and approximate transition to boson picture. Using exact transformation from paulions to bosons, the collective properties of an ideal three-dimensional gas of paulions are considered. The statistics and the collective properties of Frenkel excitons are discussed, taking into account the dynamic exciton-exciton interaction. The fermionic character of Frenkel excitons in one-dimensional molecular crystals is demonstrated.
Bas C. van Fraassen
- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239802
- eISBN:
- 9780191597466
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239807.003.0012
- Subject:
- Philosophy, Philosophy of Science
This chapter aims to place the discussion of holism in quantum theory generally and of the problem of identical particles and quantum statistics specifically in the context of general philosophy. ...
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This chapter aims to place the discussion of holism in quantum theory generally and of the problem of identical particles and quantum statistics specifically in the context of general philosophy. Various debates in metaphysics, both historical and current, broach related subjects and involve analyses of concepts currently used in the philosophy of quantum mechanics. These include concepts of identity, individuation, essence, form, necessity, possibility, modality, contingency, and universality. But this chapter also extends the previous one by introducing Fock space and the transition from elementary quantum mechanics to quantum field theory via 'second quantization’. For this formalism relates clearly to certain ’anti‐essentialist’ approaches in the metaphysics of modality. Finally, in keeping with the empiricism pursued in this book, the general enterprise of metaphysics pertaining to those topics is viewed here within an anti‐metaphysical stance, as having as its value the display of a plurality of interpretations whose very diversity enhances our understanding of the theory.Less
This chapter aims to place the discussion of holism in quantum theory generally and of the problem of identical particles and quantum statistics specifically in the context of general philosophy. Various debates in metaphysics, both historical and current, broach related subjects and involve analyses of concepts currently used in the philosophy of quantum mechanics. These include concepts of identity, individuation, essence, form, necessity, possibility, modality, contingency, and universality. But this chapter also extends the previous one by introducing Fock space and the transition from elementary quantum mechanics to quantum field theory via 'second quantization’. For this formalism relates clearly to certain ’anti‐essentialist’ approaches in the metaphysics of modality. Finally, in keeping with the empiricism pursued in this book, the general enterprise of metaphysics pertaining to those topics is viewed here within an anti‐metaphysical stance, as having as its value the display of a plurality of interpretations whose very diversity enhances our understanding of the theory.
Nikolai B. Kopnin
- Published in print:
- 2001
- Published Online:
- January 2010
- ISBN:
- 9780198507888
- eISBN:
- 9780191709722
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507888.003.02
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter introduces the second quantization formalism based on Schrödinger and Heisenberg operators. It defines the temperature and real-time Green functions for Bose and Fermi particles and ...
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This chapter introduces the second quantization formalism based on Schrödinger and Heisenberg operators. It defines the temperature and real-time Green functions for Bose and Fermi particles and discusses their analytical properties.Less
This chapter introduces the second quantization formalism based on Schrödinger and Heisenberg operators. It defines the temperature and real-time Green functions for Bose and Fermi particles and discusses their analytical properties.
Vladimir Agranovich
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199234417
- eISBN:
- 9780191715426
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234417.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This book details the studies of the properties of electronic and vibrational excitations in organic solids. It brings together most of the theory in this field together with many illustrations of ...
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This book details the studies of the properties of electronic and vibrational excitations in organic solids. It brings together most of the theory in this field together with many illustrations of experiments. There is a detailed treatment of many topics in uniform style, and the book also contains discussions of new phenomena. In different chapters, the theory of the Frenkel excitons, charge transfer excitons and polaritons, and their contribution to the optical properties of organic solids (bulk, superlattices, surfaces, nanostructures) will be found. The surface electronic excitations, optical biphonons, and Fermiresonance by polaritons are also discussed. The book presents the theory of hybrid Frenkel-Wannier-Mott excitons in nanostructures, the theory of polaritons in organic microcavities including hybrid microcavities, the new concept for LED, the effects of mixing of Frenkel and charge-transfer excitons, and the theory of excitons, and polaritons in one- and two-dimensional crystals. There are plenty of references to current research and to important historical work.Less
This book details the studies of the properties of electronic and vibrational excitations in organic solids. It brings together most of the theory in this field together with many illustrations of experiments. There is a detailed treatment of many topics in uniform style, and the book also contains discussions of new phenomena. In different chapters, the theory of the Frenkel excitons, charge transfer excitons and polaritons, and their contribution to the optical properties of organic solids (bulk, superlattices, surfaces, nanostructures) will be found. The surface electronic excitations, optical biphonons, and Fermiresonance by polaritons are also discussed. The book presents the theory of hybrid Frenkel-Wannier-Mott excitons in nanostructures, the theory of polaritons in organic microcavities including hybrid microcavities, the new concept for LED, the effects of mixing of Frenkel and charge-transfer excitons, and the theory of excitons, and polaritons in one- and two-dimensional crystals. There are plenty of references to current research and to important historical work.
Efstratios Manousakis
- Published in print:
- 2015
- Published Online:
- December 2015
- ISBN:
- 9780198749349
- eISBN:
- 9780191813474
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198749349.003.0025
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter discusses the case of a many-body system of identical particles. It considers the consequencies of the symmetry of the Hamiltonian under particle permutations in this case. It discusses ...
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This chapter discusses the case of a many-body system of identical particles. It considers the consequencies of the symmetry of the Hamiltonian under particle permutations in this case. It discusses how to build many-body Boson and Fermion states. It then introduces the formalism of so-called second quantization, which is usefu, in the case of identical particles. It also expresses the many-body Hamiltonian in terms of creation and annihilation operators.Less
This chapter discusses the case of a many-body system of identical particles. It considers the consequencies of the symmetry of the Hamiltonian under particle permutations in this case. It discusses how to build many-body Boson and Fermion states. It then introduces the formalism of so-called second quantization, which is usefu, in the case of identical particles. It also expresses the many-body Hamiltonian in terms of creation and annihilation operators.
Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199232710
- eISBN:
- 9780191774973
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232710.003.0010
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter analyzes issues that deal with quantum statistics (symmetry of wavefunctions); elements of the second quantization formalism (the occupation-number representation); and the simplest ...
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This chapter analyzes issues that deal with quantum statistics (symmetry of wavefunctions); elements of the second quantization formalism (the occupation-number representation); and the simplest systems with a large number of particles.Less
This chapter analyzes issues that deal with quantum statistics (symmetry of wavefunctions); elements of the second quantization formalism (the occupation-number representation); and the simplest systems with a large number of particles.
Anthony Duncan
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199573264
- eISBN:
- 9780191743313
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573264.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Chapter 5 discussed two possible approaches to constructing a relativistically invariant theory of particle scattering. The first attempt — a frontal assault in which one directly writes down for ...
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Chapter 5 discussed two possible approaches to constructing a relativistically invariant theory of particle scattering. The first attempt — a frontal assault in which one directly writes down for each scattering sector (i.e., with a specified number of incoming and outgoing particles) a manifestly Lorentz-invariant interaction operator containing momentum-dependent Lorentz scalar amplitudes — led to disaster. The resultant theory led to particle interactions which could not be confined to finite regions of space-time. The second attempt, in which the interaction Hamiltonian is written as a spatial integral of a local, Lorentz (ultra-)scalar field, accomplishes the primary goal of producing a Lorentz-invariant set of scattering amplitudes, but its compliance with the clustering principle remains uncertain. This chapter puts this latter requirement into a precise mathematical framework, called second quantization, so that the process of identifying clustering relativistic scattering theories can be simplified and even to some degree automated.Less
Chapter 5 discussed two possible approaches to constructing a relativistically invariant theory of particle scattering. The first attempt — a frontal assault in which one directly writes down for each scattering sector (i.e., with a specified number of incoming and outgoing particles) a manifestly Lorentz-invariant interaction operator containing momentum-dependent Lorentz scalar amplitudes — led to disaster. The resultant theory led to particle interactions which could not be confined to finite regions of space-time. The second attempt, in which the interaction Hamiltonian is written as a spatial integral of a local, Lorentz (ultra-)scalar field, accomplishes the primary goal of producing a Lorentz-invariant set of scattering amplitudes, but its compliance with the clustering principle remains uncertain. This chapter puts this latter requirement into a precise mathematical framework, called second quantization, so that the process of identifying clustering relativistic scattering theories can be simplified and even to some degree automated.
Tom Lancaster and Stephen J. Blundell
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in ...
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Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aimed to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur possessing a curious and adaptable mind looking to be told an entertaining and intellectually stimulating story, but who will not feel patronized if a few mathematical niceties are spelled out in detail.Less
Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aimed to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur possessing a curious and adaptable mind looking to be told an entertaining and intellectually stimulating story, but who will not feel patronized if a few mathematical niceties are spelled out in detail.
Tom Lancaster and Stephen J. Blundell
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
The simple harmonic oscillator is well known from basic quantum physics as an elementary model of an oscillating system. The chapter solves this simple model using creation and annihilation operators ...
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The simple harmonic oscillator is well known from basic quantum physics as an elementary model of an oscillating system. The chapter solves this simple model using creation and annihilation operators and shows that the solutions have the characteristics of particles. Linking masses by springs into a chain allows for a generalization of this problem and the solutions are phonons.Less
The simple harmonic oscillator is well known from basic quantum physics as an elementary model of an oscillating system. The chapter solves this simple model using creation and annihilation operators and shows that the solutions have the characteristics of particles. Linking masses by springs into a chain allows for a generalization of this problem and the solutions are phonons.
Tom Lancaster and Stephen J. Blundell
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter considers how to build single-particle operators out of creation and annihilation operators, and this already gives enough information to discuss the tight-binding model of solid state ...
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This chapter considers how to build single-particle operators out of creation and annihilation operators, and this already gives enough information to discuss the tight-binding model of solid state physics and the Hubbard model.Less
This chapter considers how to build single-particle operators out of creation and annihilation operators, and this already gives enough information to discuss the tight-binding model of solid state physics and the Hubbard model.
Norman J. Morgenstern Horing
- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198791942
- eISBN:
- 9780191834165
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198791942.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized ...
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Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.Less
Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.
William Barford
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199677467
- eISBN:
- 9780191757402
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199677467.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials
Semi-empirical π‐electron theories of conjugated polymers are introduced, starting from the fundamentals of the Born-Oppenheimer approximation and sp-hybridization. The models described include the ...
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Semi-empirical π‐electron theories of conjugated polymers are introduced, starting from the fundamentals of the Born-Oppenheimer approximation and sp-hybridization. The models described include the simplest non-interacting (Hückel) theory, models of electron-nuclear coupling (i.e., the Su-Schrieffer-Heeger and Peierls models), and models of interacting electrons (i.e., the Pariser-Parr-Pople model). All of them are introduced in the second quantized notation.There is also a brief discussion of the role of spatial and electron-hole symmetries, and quantum numbers in classifying the electronic states of π‐ conjugated polymers.Less
Semi-empirical π‐electron theories of conjugated polymers are introduced, starting from the fundamentals of the Born-Oppenheimer approximation and sp-hybridization. The models described include the simplest non-interacting (Hückel) theory, models of electron-nuclear coupling (i.e., the Su-Schrieffer-Heeger and Peierls models), and models of interacting electrons (i.e., the Pariser-Parr-Pople model). All of them are introduced in the second quantized notation.There is also a brief discussion of the role of spatial and electron-hole symmetries, and quantum numbers in classifying the electronic states of π‐ conjugated polymers.
Bryan J. Dalton, John Jeffers, and Stephen M. Barnett
- Published in print:
- 2014
- Published Online:
- April 2015
- ISBN:
- 9780199562749
- eISBN:
- 9780191747311
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562749.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics
This chapter sets out the second-quantisation treatment for systems of identical bosons or fermions. Key features such as the symmetrisation principle and super-selection rules are presented. ...
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This chapter sets out the second-quantisation treatment for systems of identical bosons or fermions. Key features such as the symmetrisation principle and super-selection rules are presented. Orthogonality and completeness requirements for mode functions are set out, and Fock states are defined in terms of mode occupancy, leading to the definitions of mode annihilation and creation operators and the determination of their commutation (bosons) or anticommutation (fermions) rules. Important two-mode states such as binomial states and relative-phase eigenstates are considered. Field creation and annihilation operators are defined and related to multi-particle position eigenstates. The Hamiltonian is expressed in terms of both mode operators and field operators, state dynamics being treated via Liouville–von Neumann, master or Matsubara equations for the density operator. Normal ordering is introduced and applied to expressions for the vacuum state projector. Multi-particle position probabilities are considered and related to normally ordered quantum correlation functions.Less
This chapter sets out the second-quantisation treatment for systems of identical bosons or fermions. Key features such as the symmetrisation principle and super-selection rules are presented. Orthogonality and completeness requirements for mode functions are set out, and Fock states are defined in terms of mode occupancy, leading to the definitions of mode annihilation and creation operators and the determination of their commutation (bosons) or anticommutation (fermions) rules. Important two-mode states such as binomial states and relative-phase eigenstates are considered. Field creation and annihilation operators are defined and related to multi-particle position eigenstates. The Hamiltonian is expressed in terms of both mode operators and field operators, state dynamics being treated via Liouville–von Neumann, master or Matsubara equations for the density operator. Normal ordering is introduced and applied to expressions for the vacuum state projector. Multi-particle position probabilities are considered and related to normally ordered quantum correlation functions.
Tom Lancaster and Stephen J. Blundell
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter changes our viewpoint and get rid of wave functions entirely and develops the occupation number representation. The chapter shows that bosons are described by commuting operators and ...
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This chapter changes our viewpoint and get rid of wave functions entirely and develops the occupation number representation. The chapter shows that bosons are described by commuting operators and fermions are described by anticommuting operators.Less
This chapter changes our viewpoint and get rid of wave functions entirely and develops the occupation number representation. The chapter shows that bosons are described by commuting operators and fermions are described by anticommuting operators.
