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), 2024. Published by Science Publishing Group |
Wave Problem, Riccatti’s Equation, Quantization Condition
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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
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
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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Download@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}
}
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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