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Field quantization

J. C. Garrison and R. Y. Chiao

in Quantum Optics

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198508861
eISBN:
9780191708640
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508861.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

The cavity-mode quantization conjecture of Chapter 2 is replaced by local commutation relations — which are independent of the size and shape of the cavity — between field-operator components. This ... More


Quantization of cavity modes

J. C. Garrison and R. Y. Chiao

in Quantum Optics

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198508861
eISBN:
9780191708640
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508861.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter begins with a normal-mode analysis of the classical electromagnetic field in an ideal cavity. The resulting expression for the electromagnetic energy has the same form as the energy of a ... More


Angular Momentum

Gary E. Bowman

in Essential Quantum Mechanics

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228928
eISBN:
9780191711206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228928.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

Angular momentum is one of the more abstract topics in quantum mechanics. This chapter begins with a review of classical angular momentum. Quantum-mechanical angular momentum is then introduced by ... More


Quantizing

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0002
Subject:
Philosophy, Philosophy of Science

This chapter explicates the Hamiltonian scheme for quantizing classical mechanical theories by finding a Hilbert space representation of the appropriate canonical commutation relations. The chapter ... More


Hyperbolic geometry

Jacques Franchi and Yves Le Jan

in Hyperbolic Dynamics and Brownian Motion: An Introduction

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199654109
eISBN:
9780191745676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199654109.003.0002
Subject:
Mathematics, Mathematical Physics

Basic notions of hyperbolic geometry are presented: geodesics, light rays, tangent bundles etc. These are systematically derived from properties of Minkowski space: the boundary of hyperbolic space ... More


Identical Particles and Second Quantization: Occupation Number Representation

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/9780198791942.003.0002
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 ... More


Two-State Systems: The Atomic Operators

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/9780192895073.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

In the digital world, the concepts of on and off or high and low or 0 and 1 are common classical two-state systems. Quantum systems can be similarly configured, as we saw in Chapter 9 with the ... More


Angular Momentum and the Quantum Gyroscope: The Emergence of 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/9780192895073.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Continuing with understanding the implications of the postulates in Chapter 7 and following the approach in Chapter 8 to use operators find solutions to the time independent Schrödinger equation, we ... More


Elements of quantum theory

Stephen Barnett

in Quantum Information

Published in print:
2009
Published Online:
November 2020
ISBN:
9780198527626
eISBN:
9780191916625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198527626.003.0005
Subject:
Computer Science, Mathematical Theory of Computation

We have seen that there is an intimate relationship between probability and information. The values we assign to probabilities depend on the information available, and information is a function of ... More


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