
Contents
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3.1 The Harmonic Oscillator 3.1 The Harmonic Oscillator
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3.1.1 Zero-Point Energy 3.1.1 Zero-Point Energy
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3.2 Field Hamiltonian 3.2 Field Hamiltonian
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3.3 Field Quantization: Energy and Momentum 3.3 Field Quantization: Energy and Momentum
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3.3.1 Linear Momentum 3.3.1 Linear Momentum
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3.3.2 Angular Momentum (Spin) 3.3.2 Angular Momentum (Spin)
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3.4 Quantized Fields in Dielectric Media 3.4 Quantized Fields in Dielectric Media
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3.5 Photons and Interference 3.5 Photons and Interference
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3.6 Quantum States of the Field and Their Statistical Properties 3.6 Quantum States of the Field and Their Statistical Properties
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3.6.1 Coherent States 3.6.1 Coherent States
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3.6.2 Classically Prescribed Sources 3.6.2 Classically Prescribed Sources
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3.6.3 Laser Light 3.6.3 Laser Light
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3.6.4 Squeezed States 3.6.4 Squeezed States
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3.6.5 Thermal and Chaotic Radiation 3.6.5 Thermal and Chaotic Radiation
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3.6.6 Mandel’s Q Parameter 3.6.6 Mandel’s Q Parameter
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3.6.7 Photon Counting 3.6.7 Photon Counting
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3.7 The Density Operator 3.7 The Density Operator
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3.7.1 Characteristic Function 3.7.1 Characteristic Function
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3.7.2 Generating Function for Photon Number Probability 3.7.2 Generating Function for Photon Number Probability
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3.8 Coherent-State Representation of the Density Operator 3.8 Coherent-State Representation of the Density Operator
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3.9 Correlation Functions 3.9 Correlation Functions
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3.10 Field Commutators and Uncertainty Relations 3.10 Field Commutators and Uncertainty Relations
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3.11 Complementarity: Wave and Particle Descriptions of Light 3.11 Complementarity: Wave and Particle Descriptions of Light
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3.12 More on Uncertainty Relations 3.12 More on Uncertainty Relations
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2.12.1 Simultaneous Measurement of Non-Commuting Observables 2.12.1 Simultaneous Measurement of Non-Commuting Observables
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3.12.2 Energy–Time Uncertainty Relations 3.12.2 Energy–Time Uncertainty Relations
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References and Suggested Additional Reading References and Suggested Additional Reading
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3 Quantum Theory of the Electromagnetic Field
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Published:January 2019
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Abstract
The electromagnetic field is quantized for free space and for dispersive dielectric media. Different quantum states of the field (thermal, laser, squeezed) are discussed and their photon-statistical properties derived. The density matrix operator for the field is introduced along with a detailed discussion of the diagonal representation of the field density operator and its properties. Field commutation relations, correlation functions, and uncertainty relations are derived and discussed. Also discussed are the historically important Bohr-Rosenfeld analysis of field commutation and uncertainty relations; energy-time uncertainty relations; simultaneous (Arthurs-Kelly) measurement of non-commuting observables; and complementarity from the perspective of probability amplitudes and probabilities for distinguishable and indistinguishable processes.
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