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Quantum Statistical Field TheoryAn Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity$
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Norman J. Morgenstern Horing

Print publication date: 2017

Print ISBN-13: 9780198791942

Published to Oxford Scholarship Online: January 2018

DOI: 10.1093/oso/9780198791942.001.0001

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Identical Particles and Second Quantization: Occupation Number Representation

Identical Particles and Second Quantization: Occupation Number Representation

Chapter:
(p.20) 2 Identical Particles and Second Quantization: Occupation Number Representation
Source:
Quantum Statistical Field Theory
Author(s):

Norman J. Morgenstern Horing

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198791942.003.0002

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.

Keywords:   many identical particles, Pauli exclusion principle, Schwinger measurement symbols, creation/annihilation operators, commutation/anticommutation relations, second quantization, Hamiltonian operator, number operator, linear and angular momentum operators, coherent states

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