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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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