New Solution Method of Wave Problems from the Turning Points
International Journal of Energy and Power Engineering
Volume 3, Issue 1, February 2014, Pages: 15-20
Received: Jan. 21, 2014; Published: Feb. 20, 2014
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Authors
Kamal Sheikh Younis, Department of Electrical Engineering, Salahaddin University, Erbil, Iraq
Nikolay Evgenevich Tsapenko, Department of Mathematics, Moscow State Mining University
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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.
Keywords
Wave Problem, Riccatti’s Equation, Quantization Condition
To cite this article
Kamal Sheikh Younis, Nikolay Evgenevich Tsapenko, New Solution Method of Wave Problems from the Turning Points, International Journal of Energy and Power Engineering. Vol. 3, No. 1, 2014, pp. 15-20. doi: 10.11648/j.ijepe.20140301.13
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