On the Problem of Electromagnetic-Field Quantization

Christian Krattenthaler; Sergey I. Kryuchkov; Alex Mahalov; Sergei Suslov

doi:10.1007/s10773-013-1764-3

On the Problem of Electromagnetic-Field Quantization

Christian Krattenthaler, Sergey I. Kryuchkov, Alex Mahalov, Sergei Suslov

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional quadratic Hamiltonian. Explicit solutions of these equations are obtained and applications to the radiation field quantization, including randomly varying media, are briefly discussed.

Original language	English (US)
Pages (from-to)	4445-4460
Number of pages	16
Journal	International Journal of Theoretical Physics
Volume	52
Issue number	12
DOIs	https://doi.org/10.1007/s10773-013-1764-3
State	Published - Dec 2013

Keywords

Berry's phase
Bogoliubov transformation
Dynamic invariants
Generalized harmonic oscillators
Heisenberg equations of motion
Minimum-uncertainty squeezed states
Quantization in randomly varying media
Radiation field operators
Time-dependent Schrödinger equation
Uncertainty relation

ASJC Scopus subject areas

General Mathematics
Physics and Astronomy (miscellaneous)

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10.1007/s10773-013-1764-3

Cite this

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title = "On the Problem of Electromagnetic-Field Quantization",

abstract = "We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional quadratic Hamiltonian. Explicit solutions of these equations are obtained and applications to the radiation field quantization, including randomly varying media, are briefly discussed.",

keywords = "Berry's phase, Bogoliubov transformation, Dynamic invariants, Generalized harmonic oscillators, Heisenberg equations of motion, Minimum-uncertainty squeezed states, Quantization in randomly varying media, Radiation field operators, Time-dependent Schr{\"o}dinger equation, Uncertainty relation",

author = "Christian Krattenthaler and Kryuchkov, {Sergey I.} and Alex Mahalov and Sergei Suslov",

note = "Funding Information: Acknowledgements We thank Michael Berry for bringing Ref. [5] to our attention and Victor Dodonov and Luc Vinet for valuable discussions. This research was partially supported by an AFOSR grant FA9550-11-1-0220 and by the Austrian Science Foundation FWF, grants Z130-N13 and S50-N15, the latter in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”.",

year = "2013",

month = dec,

doi = "10.1007/s10773-013-1764-3",

language = "English (US)",

volume = "52",

pages = "4445--4460",

journal = "International Journal of Theoretical Physics",

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publisher = "Springer New York",

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T1 - On the Problem of Electromagnetic-Field Quantization

AU - Krattenthaler, Christian

AU - Kryuchkov, Sergey I.

AU - Mahalov, Alex

AU - Suslov, Sergei

N1 - Funding Information: Acknowledgements We thank Michael Berry for bringing Ref. [5] to our attention and Victor Dodonov and Luc Vinet for valuable discussions. This research was partially supported by an AFOSR grant FA9550-11-1-0220 and by the Austrian Science Foundation FWF, grants Z130-N13 and S50-N15, the latter in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”.

PY - 2013/12

Y1 - 2013/12

N2 - We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional quadratic Hamiltonian. Explicit solutions of these equations are obtained and applications to the radiation field quantization, including randomly varying media, are briefly discussed.

AB - We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional quadratic Hamiltonian. Explicit solutions of these equations are obtained and applications to the radiation field quantization, including randomly varying media, are briefly discussed.

KW - Berry's phase

KW - Bogoliubov transformation

KW - Dynamic invariants

KW - Generalized harmonic oscillators

KW - Heisenberg equations of motion

KW - Minimum-uncertainty squeezed states

KW - Quantization in randomly varying media

KW - Radiation field operators

KW - Time-dependent Schrödinger equation

KW - Uncertainty relation

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EP - 4460

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

IS - 12

ER -

On the Problem of Electromagnetic-Field Quantization

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Keywords

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