International Journal of Theoretical Physics

, Volume 52, Issue 12, pp 4445–4460 | Cite as

On the Problem of Electromagnetic-Field Quantization

  • Christian Krattenthaler
  • Sergey I. Kryuchkov
  • Alex Mahalov
  • Sergei K. Suslov


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.


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



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”.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Christian Krattenthaler
    • 1
  • Sergey I. Kryuchkov
    • 2
  • Alex Mahalov
    • 2
  • Sergei K. Suslov
    • 2
  1. 1.Fakultät für MathematikUniversität WienViennaAustria
  2. 2.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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