Eigenvalues of the Schrödinger Equation for a Periodic Potential

Abdulla Jameel Sous

doi:doi:10.11648/j.ajmp.20150406.16

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Eigenvalues of the Schrödinger Equation for a Periodic Potential

Abdulla Jameel Sous

Published in American Journal of Modern Physics (Volume 4, Issue 6)

Received: 11 December 2015 Accepted: 23 December 2015 Published: 4 January 2016

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Abstract

By studying the application of the asymptotic iteration method, we found a new numerical results of the eigenvalues for non-quasi-exactly solvable periodic potential. In addition to that, the results we get for quasi-exactly solvable solution are typical to the results achieved by Qiong-Tao Xie [J. Phys. A: Math. Theor. 44 (2011) 285302].

Published in	American Journal of Modern Physics (Volume 4, Issue 6)
DOI	10.11648/j.ajmp.20150406.16
Page(s)	291-295
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), 2016. Published by Science Publishing Group

Keywords

Periodic Potential, Asymptotic Iteration Method, Eigenvalues E_n

References

[1]	Lihui Cha, Shi Jin, Qin Li, American Institute of Mathematical Sciences, Vol 6, Issue 3, September 2013.
[2]	Kirstine Berg-Sørensen and Klaus Mølmer, Phys. Rev. A 58, 1480, 1998.
[3]	K. G. Makris, R. El-Ganainy, D. N. Christodoulides, nt J Theor Phys (2011) 50: 1019–1041.
[4]	M. Salerno, V. V. Konotop, and Yu. V. Bludov, Phys. Rev. Lett. 101, 030405, 2008.
[5]	Turbiner, A., Phys. Rev, A 50 5335 (1994).
[6]	Turbiner A V 1988 Commun. Math. Phys. 118 467.
[7]	Shifman M A 1989 Int. J. Mod. Phys. A 4 3305.
[8]	Kamran N and Olver P J 1990 J. Math. Anal. Appl. 145 342.
[9]	Ulyanov V V and Zaslavskii O B 1992 Phys. Rep. 216 179.
[10]	A, J, sous, Modern Physics Letters A, Vol. 22, No. 22 (2007).
[11]	M. Razavy, Phys. Lett. A 72, 89 (1979).
[12]	M. Razavy, Am. J. Phys. 48, 285 (1980).
[13]	Bartolomeu D B F 2002 J. Phys. A: Math. Gen. 35 2877.
[14]	A. Khare, S. Habib and A. Saxena, Phys. Rev. Lett. 79, 3797 (1997).
[15]	Fedele F, Yang J and Chen Z 2005 Opt. Lett. 30 1506.
[16]	Yang J and Chen Z 2006 Phys. Rev. E 73 026609.
[17]	Bei-Hua Chen, Yan Wu and Qiong-Tao Xie, J. Phys. A: Math. Theor. 46 (2013) 035301.
[18]	Qiong-Tao Xie, J. Phys. A: Math. Theor. 44 (2011) 285302.
[19]	H. Çiftci, R. L. Hall, N. Saad, J. Phys. A 36, 11807 (2003).
[20]	Ramazan Koç, Eser Olğar, and Haydar Mutaf. Adv. in Math. Phys. Vol. 2015 (2015),
[21]	N. Saad, R. L. Hall, H. Çiftci, J. Phys. A 39, 8477 (2006).
[22]	Abdallah J. Sous, Journal of Applied Mathematics and Physics, 3, (2015).
[23]	Marwan Izzat El-Kawni, Abdulla Jameel Sous, American Journal of Modern Physics. Vol. 4, No. 1, (2015).

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Abdulla Jameel Sous. (2016). Eigenvalues of the Schrödinger Equation for a Periodic Potential. American Journal of Modern Physics, 4(6), 291-295. https://doi.org/10.11648/j.ajmp.20150406.16

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Abdulla Jameel Sous. Eigenvalues of the Schrödinger Equation for a Periodic Potential. Am. J. Mod. Phys. 2016, 4(6), 291-295. doi: 10.11648/j.ajmp.20150406.16

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Abdulla Jameel Sous. Eigenvalues of the Schrödinger Equation for a Periodic Potential. Am J Mod Phys. 2016;4(6):291-295. doi: 10.11648/j.ajmp.20150406.16

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@article{10.11648/j.ajmp.20150406.16,
  author = {Abdulla Jameel Sous},
  title = {Eigenvalues of the Schrödinger Equation for a Periodic Potential},
  journal = {American Journal of Modern Physics},
  volume = {4},
  number = {6},
  pages = {291-295},
  doi = {10.11648/j.ajmp.20150406.16},
  url = {https://doi.org/10.11648/j.ajmp.20150406.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20150406.16},
  abstract = {By studying the application of the asymptotic iteration method, we found a new numerical results of the eigenvalues for non-quasi-exactly solvable periodic potential. In addition to that, the results we get for quasi-exactly solvable solution are typical to the results achieved by Qiong-Tao Xie [J. Phys. A: Math. Theor. 44 (2011) 285302].},
 year = {2016}
}

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TY  - JOUR
T1  - Eigenvalues of the Schrödinger Equation for a Periodic Potential
AU  - Abdulla Jameel Sous
Y1  - 2016/01/04
PY  - 2016
N1  - https://doi.org/10.11648/j.ajmp.20150406.16
DO  - 10.11648/j.ajmp.20150406.16
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 291
EP  - 295
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20150406.16
AB  - By studying the application of the asymptotic iteration method, we found a new numerical results of the eigenvalues for non-quasi-exactly solvable periodic potential. In addition to that, the results we get for quasi-exactly solvable solution are typical to the results achieved by Qiong-Tao Xie [J. Phys. A: Math. Theor. 44 (2011) 285302].
VL  - 4
IS  - 6
ER  -

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Author Information

Abdulla Jameel Sous

Department of Mathematics, Faculty of Technology and Applied Sciences, Al-Quds Open University, Tulkarm, Palestine

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Abdulla Jameel Sous. (2016). Eigenvalues of the Schrödinger Equation for a Periodic Potential. American Journal of Modern Physics, 4(6), 291-295. https://doi.org/10.11648/j.ajmp.20150406.16

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ACS Style

Abdulla Jameel Sous. Eigenvalues of the Schrödinger Equation for a Periodic Potential. Am. J. Mod. Phys. 2016, 4(6), 291-295. doi: 10.11648/j.ajmp.20150406.16

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AMA Style

Abdulla Jameel Sous. Eigenvalues of the Schrödinger Equation for a Periodic Potential. Am J Mod Phys. 2016;4(6):291-295. doi: 10.11648/j.ajmp.20150406.16

Copy | Download

@article{10.11648/j.ajmp.20150406.16,
  author = {Abdulla Jameel Sous},
  title = {Eigenvalues of the Schrödinger Equation for a Periodic Potential},
  journal = {American Journal of Modern Physics},
  volume = {4},
  number = {6},
  pages = {291-295},
  doi = {10.11648/j.ajmp.20150406.16},
  url = {https://doi.org/10.11648/j.ajmp.20150406.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20150406.16},
  abstract = {By studying the application of the asymptotic iteration method, we found a new numerical results of the eigenvalues for non-quasi-exactly solvable periodic potential. In addition to that, the results we get for quasi-exactly solvable solution are typical to the results achieved by Qiong-Tao Xie [J. Phys. A: Math. Theor. 44 (2011) 285302].},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Eigenvalues of the Schrödinger Equation for a Periodic Potential
AU  - Abdulla Jameel Sous
Y1  - 2016/01/04
PY  - 2016
N1  - https://doi.org/10.11648/j.ajmp.20150406.16
DO  - 10.11648/j.ajmp.20150406.16
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 291
EP  - 295
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20150406.16
AB  - By studying the application of the asymptotic iteration method, we found a new numerical results of the eigenvalues for non-quasi-exactly solvable periodic potential. In addition to that, the results we get for quasi-exactly solvable solution are typical to the results achieved by Qiong-Tao Xie [J. Phys. A: Math. Theor. 44 (2011) 285302].
VL  - 4
IS  - 6
ER  -

Copy | Download