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Peculiarities of passage of an oscillator through a potential barrier

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Russian Physics Journal Aims and scope

The problem of passage of a classical oscillator through a potential barrier is solved. Nonlinear sub-barrier passage and above-barrier reflection of the oscillator with elements of energy quantization are revealed. Within the framework of the laws of classical mechanics, an explanation is proposed for the obtained regularities of motion of the oscillator. The results not only enable an extension of the region of applicability of the laws of classical mechanics, but also reveal the essence of its limitations due to the requirement of holonomic couplings in the Lagrangian and Hamiltonian formalisms.

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References

  1. L. I. Mandel’shtam, Lectures on the Theory of Oscillations [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  2. G. M. Zaslavskii, Stochasticity of Dynamic Systems [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  3. V. B. Berestetskii, L. P. Pitaevskii, and E. M. Lifshitz, Quantum Electrodynamics, Second Edition, Elsevier, Cambridge, Massachusetts (1982).

    Google Scholar 

  4. M. G. Rosenblum and A. S. Pikovsky, Phys. Rev., E64, 045202 (2001).

    ADS  Google Scholar 

  5. V. M. Somsikov, J. Mater. Sci. Eng., A1, 731–740 (2011).

    Google Scholar 

  6. V. M. Somsikov, Probl. Evol. Otkryt. Sist., 2, No. 12, 3–17 (2010).

    Google Scholar 

  7. V. M. Somsikov, New Adv. Phys., 2, No. 2, 125–140 (2008).

    Google Scholar 

  8. H. Goldstein, Classical Mechanics, Second Edition, Addison-Wesley, Reading, Massachusetts (1980).

    MATH  Google Scholar 

  9. C. Lanczos, The Variational Principles of Mechanics, The University of Toronto Press, Toronto; Fourth Edition, Dover Paperback, Dover Publishing, Mineola; New York (1974).

  10. A. B. Migdal, Qualitative Methods in Quantum Theory, Westview Press, Boulder, Colorado (2000).

    Google Scholar 

  11. S. Goldstein, Phys. Today, No. 3, 42–46 (1998).

  12. S. Goldstein, Phys. Today, No. 3, 38–42 (1998).

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Authors and Affiliations

  1. Institute of Ionosphere, Almaty, Kazakhstan

    V. M. Somsikov & M. I. Denisenya

Authors
  1. V. M. Somsikov
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  2. M. I. Denisenya
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Correspondence to V. M. Somsikov.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 95–103, April, 2013.

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Somsikov, V.M., Denisenya, M.I. Peculiarities of passage of an oscillator through a potential barrier. Russ Phys J 56, 463–472 (2013). https://doi.org/10.1007/s11182-013-0056-y

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  • DOI: https://doi.org/10.1007/s11182-013-0056-y

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