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An electron in a quantized plane wave and in a constant magnetic field

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Zeitschrift für Physik A Hadrons and nuclei

Abstract

The Dirac equation is considered for an electron in a constant homogeneous magnetic field and in a quantized electromagnetic plane wave propagating along the direction of the former. This problem is shown to be reduced to the Schrödinger equation for a system of many interacting oscillators. The corresponding Hamiltonian is diagonalized. An equation is established relating the total energy with the moment of a system along the magnetic field. Approximate solutions of this equation are given. A behaviour of a system close to cyclotron resonance is discussed.

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References

  1. Eberly, T. H.: Progr. opt.7, 359 (1969).

    Article  Google Scholar 

  2. Bunkin, F. V., Kazakov, A. E., Fedorov, M. V.: UFN107, 559 (1972). Moscow, USSR.

    Article  Google Scholar 

  3. Berson, I. Ya.: JETP, USSR56, 1627 (1969).

    MathSciNet  Google Scholar 

  4. Berson, I. Ya.: Izv. Acad. Nauk Latv. SSR, USSR, No 3, 4 (1970).

    Google Scholar 

  5. Gazasyan, A. D.: The Journ. of Theor. and Math. Phys., USSR10, 388 (1972).

    Google Scholar 

  6. Berson, I. Ya.: Izv. Acad. Nauk Latv. SSR, USSR, No 5, 3 (1969).

    Google Scholar 

  7. Abakarov, D. I., Oleinik, V. P.: The Journ. of Theor. and Math. Phys., USSR12, 78 (1972).

    Google Scholar 

  8. Kazakov, A. E., Fedorov, M. V.: Short Rep., FIAN, USSR11, 42 (1972).

    Google Scholar 

  9. Berson, I. Ya.: J. Math. Phys., to be published.

  10. Achiezer, A. I., Berestetsky, V. B.: Quantum electrodynamics. Moscow, USSR: FIZMATGHIZ 1959.

    Google Scholar 

  11. Davidov, A. S.: Quantum mechanics. Moscow, USSR: FIZMATGHIZ 1963.

    Google Scholar 

  12. Landau, L. D., Lifshitz, E. M.: Mechanics. Moscow, USSR: FIZMATHGIZ 1958.

    MATH  Google Scholar 

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Authors and Affiliations

  1. P. N. Lebedev Physical Institute of the Academy of Sciences of the USSR, Moscow

    M. V. Fedorov & A. E. Kazakov

Authors
  1. M. V. Fedorov
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  2. A. E. Kazakov
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Fedorov, M.V., Kazakov, A.E. An electron in a quantized plane wave and in a constant magnetic field. Z. Physik 261, 191–202 (1973). https://doi.org/10.1007/BF01391912

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  • DOI: https://doi.org/10.1007/BF01391912

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