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Quantum-Mechanical Problem with Periodic Initial Conditions in Classical Physics and Geometrodynamics

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Russian Physics Journal Aims and scope

It is shown that in classical physics there is a time analog of a spatial quantum-mechanical problem with periodic boundary conditions. On this basis, it is shown that the corresponding energy quantity has a band structure.

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References

  1. V. V. Lasukov, T. V. Lasukova, et al., Russ. Phys. J., 57, No. 4, 490–497 (2014).

    Article  Google Scholar 

  2. V. V. Lasukov, Int. J. Geom. Methods Mod. Phys., 13, Nо. 2, 1650020 (2016).

  3. B. S. De Witt, Phys. Rev., 160 (D), 1113 (1967).

  4. B. S. De Witt, Phys. Rev., 162 (D), 1195 (1967).

  5. B. L. Al’tshuler and A. O. Barvinskii, Usp. Fiz. Nauk, 166, 46 (1996).

    Google Scholar 

  6. A. D. Linde, Particle Physics and Inflationary Cosmology, Harwood Academic Publishers, New York (1990).

  7. J. Hartle and S. Hawking, Phys. Rev., 28, 2960 (1983).

    ADS  MathSciNet  Google Scholar 

  8. A. Vilenkin, Phys. Lett. B, 117, 25 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Linde, Phys. Lett. B, 129, 177 (1983).

    Article  ADS  Google Scholar 

  10. A. Linde, Phys. Lett. B, 108, 389 (1982).

    Article  ADS  Google Scholar 

  11. A. Starobinsky, Phys. Lett. B, 91, 99 (1980).

    Article  ADS  Google Scholar 

  12. I. G. Dymnikova, Phys. Lett. B, 472, 33 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  13. C. W. Misner and J. A. Wheeler, Ann. Phys., 2, 525–603 (1957).

    Article  ADS  Google Scholar 

  14. J. A. Wheeler, Ann. Phys., 2, 604–614 (1957).

    Article  ADS  Google Scholar 

  15. V. V. Lasukov, Russ. Phys. J., 55, No. 10, 1157–1168 (2012).

    Article  MathSciNet  Google Scholar 

  16. V. V. Lasukov and A. N. Karlova, Russ. Phys. J., 51, No. 3, 321–326 (2008).

    Article  Google Scholar 

  17. É. B. Gliner, Usp. Fiz. Nauk, 172, 221 (2002).

    Article  Google Scholar 

  18. É. B. Gliner, Zh. Eksp. Teor. Fiz., 49, 342 (1965).

    Google Scholar 

  19. É. B. Gliner, Dokl. Akad. Nauk SSSR, 192, 771 (1970).

    ADS  Google Scholar 

  20. I. G. Dymnikova, Zh. Eksp. Teor. Fiz., 90, 1900 (1986).

    ADS  Google Scholar 

  21. É. B. Gliner and I. G. Dymnikova, Pis’ma Astron. Zh., 1, 7 (1975).

  22. I. G. Dymnikova, Phys. Lett. B, 472, 33 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  23. I. G. Dymnikova, Gen. Rel. Grav., 24, 235 (1992).

    Article  ADS  Google Scholar 

  24. I. G. Dymnikova, Int. J. Mod. Phys., 5, 529 (1996).

    Article  ADS  Google Scholar 

  25. A. Olsen Haakon and Yu. P. Kunashenko, Phys. Rev. A, 56, 527–537 (1997).

    Article  ADS  Google Scholar 

  26. K. B. Korotchenko, Y. P. Kunashenko, and T. A. Tukhfatullin, Nucl. Instrum. Methods Phys. Res. B, 276, 14–18 (2012).

    Article  ADS  Google Scholar 

  27. K. B. Korotchenko and Y. P. Kunashenko, Nucl. Instrum. Methods Phys. Res. B, 309, 88–91 (2013).

    Article  ADS  Google Scholar 

  28. Y. P. Kunashenko, J. Surf. Invest. X-ray, Synchrotron and Neutron Techniques, 6, 271–276 (2012).

    Article  Google Scholar 

  29. T. A. Tukhfatullin, Y. L. Pivovarov, et al., Nucl. Instrum. Methods Phys. Res. B, 402, 236–239 (2017).

    Article  ADS  Google Scholar 

  30. V. M. Bystritsky, G. N. Dudkin, et al., Int. J. Mod. Phys. E, 26, No. 3, 1–8 (2017).

    Article  Google Scholar 

  31. G. N. Dudkin, S. I. Kuznetsov, et al., Nucl. Instrum. Methods Phys. Res. A, 875, 137–140 (2017).

    Article  ADS  Google Scholar 

  32. A. L. Potekaev, S. B. Kislitsin, et al., Russ. Phys. J., 59, No. 1, 99–108 (2016).

    Article  Google Scholar 

  33. A. I. Potekaev, A. A. Klopotov, et al., Steel in Translation, 43, 184 (2013).

    Article  Google Scholar 

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Correspondence to V. V. Lasukov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 67–71, April, 2019.

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Lasukov, V.V., Lasukova, T.V. Quantum-Mechanical Problem with Periodic Initial Conditions in Classical Physics and Geometrodynamics. Russ Phys J 62, 632–637 (2019). https://doi.org/10.1007/s11182-019-01757-1

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  • DOI: https://doi.org/10.1007/s11182-019-01757-1

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