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New Solution Method of Wave Problems from the Turning Points

Received: 21 January 2014     Published: 20 February 2014
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Abstract

One of the main challenges in wave processes is the problem of eventuality correctness of different asymptotic representations of the same exact solution taken from different sides of the turning point. In this paper a universal solution method of this problem has been developed and the particular solutions of the wave equation have been expressed in terms of the solutions of Riccati’s equation for which the proper values in the turning points have been obtained. The paper demonstrates that, just those values will breed a correct phase and amplitude correlations in wave functions. Exact quantization conditions have been deduced and exact formulas for reflection and passage coefficients of quanta mechanical particles of potential barrier have been derived.

Published in International Journal of Energy and Power Engineering (Volume 3, Issue 1)
DOI 10.11648/j.ijepe.20140301.13
Page(s) 15-20
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Wave Problem, Riccatti’s Equation, Quantization Condition

References
[1] J. Heading." An introduction to phase-integral method" Mir publishers,1965
[2] N Fröman and P.O Fröman JWKB "Approximation contribution to the theory" Amsterdam, North-Holland publishing company, 1965
[3] N.Fröman and P.O. Fröman "On Ventsel’s proof of the quantization condition for a single-wall potential". J. of Mathematical Physics. University of Uppsala, Sweden vol.18.No1, 1977, pp.96-99.
[4] N.E.Tsapenko "New formulas for approximate solution of the one-dimensional wave" .Differential Equations, 1989, Minsk, vol.25.No.11, pp.1941-1946.
[5] N.E.Tsapenko "Plane electromagnetic waves in heterogeneous medium approximation regarding relative rate of change of wave resistance". Laser and Particle Beams, 1993, vol.11No 4, pp.679-684.
[6] N.E.Tsapenko "Riccatis equation and wave processes". Moscow, MSMU, Publisher, Gornaya Kniga, 2008.
Cite This Article
  • APA Style

    Kamal Sheikh Younis, Nikolay Evgenevich Tsapenko. (2014). New Solution Method of Wave Problems from the Turning Points. International Journal of Energy and Power Engineering, 3(1), 15-20. https://doi.org/10.11648/j.ijepe.20140301.13

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    ACS Style

    Kamal Sheikh Younis; Nikolay Evgenevich Tsapenko. New Solution Method of Wave Problems from the Turning Points. Int. J. Energy Power Eng. 2014, 3(1), 15-20. doi: 10.11648/j.ijepe.20140301.13

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    AMA Style

    Kamal Sheikh Younis, Nikolay Evgenevich Tsapenko. New Solution Method of Wave Problems from the Turning Points. Int J Energy Power Eng. 2014;3(1):15-20. doi: 10.11648/j.ijepe.20140301.13

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  • @article{10.11648/j.ijepe.20140301.13,
      author = {Kamal Sheikh Younis and Nikolay Evgenevich Tsapenko},
      title = {New Solution Method of Wave Problems from the Turning Points},
      journal = {International Journal of Energy and Power Engineering},
      volume = {3},
      number = {1},
      pages = {15-20},
      doi = {10.11648/j.ijepe.20140301.13},
      url = {https://doi.org/10.11648/j.ijepe.20140301.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijepe.20140301.13},
      abstract = {One of the main challenges in wave processes is the problem of eventuality correctness of different asymptotic representations of the same exact solution taken from different sides of the turning point. In this paper a universal solution method of this problem has been developed and the particular solutions of the wave equation have been expressed in terms of the solutions of Riccati’s equation for which the proper values in the turning points have been obtained. The paper demonstrates that, just those values will breed a correct phase and amplitude correlations in wave functions. Exact quantization conditions have been deduced and exact formulas for reflection and passage coefficients of quanta mechanical particles of potential barrier have been derived.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - New Solution Method of Wave Problems from the Turning Points
    AU  - Kamal Sheikh Younis
    AU  - Nikolay Evgenevich Tsapenko
    Y1  - 2014/02/20
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ijepe.20140301.13
    DO  - 10.11648/j.ijepe.20140301.13
    T2  - International Journal of Energy and Power Engineering
    JF  - International Journal of Energy and Power Engineering
    JO  - International Journal of Energy and Power Engineering
    SP  - 15
    EP  - 20
    PB  - Science Publishing Group
    SN  - 2326-960X
    UR  - https://doi.org/10.11648/j.ijepe.20140301.13
    AB  - One of the main challenges in wave processes is the problem of eventuality correctness of different asymptotic representations of the same exact solution taken from different sides of the turning point. In this paper a universal solution method of this problem has been developed and the particular solutions of the wave equation have been expressed in terms of the solutions of Riccati’s equation for which the proper values in the turning points have been obtained. The paper demonstrates that, just those values will breed a correct phase and amplitude correlations in wave functions. Exact quantization conditions have been deduced and exact formulas for reflection and passage coefficients of quanta mechanical particles of potential barrier have been derived.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • Department of Electrical Engineering, Salahaddin University, Erbil, Iraq

  • Department of Mathematics, Moscow State Mining University

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