International Journal of Modern Physics and Applications
Articles Information
International Journal of Modern Physics and Applications, Vol.1, No.2, May 2015, Pub. Date: May 6, 2015
A Computed Solution to the Schrödinger Equation in the One-Dimensional Non-Relativistic Electron Case Using a Polynomials Expansion Scheme
Pages: 22-26 Views: 1245 Downloads: 516
Authors
[01] Ayşe Yumak, Physics Department, Faculty of Arts and Sciences, Marmara University, Istanbul, Turkey.
[02] Karem Boubaker, Unity of Physics of Semi-Conductings Disposals UPDS, Tunis EL MANAR University, Tunisia.
Abstract
In this paper, travelling wave solutions to the nonlinearly dispersive Schrödinger equation are computed in the case of one-dimensional non-relativistic electron confined to a cylindrical quantum well. Investigations gave evidence to the possibility of simplified continuous solutions which are in good agreement with the probabilistic interpretation of this equation.
Keywords
Schrödinger Equation, Non-Relativistic Electron, Quantum Well, Boubaker Polynomials Expansion Scheme BPES, Rogue-Langmuir Traveling Wave
References
[01] V. Banica, L. Vega, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 25( 4) (2008), 697
[02] P. Bégout, Jesús I. Díaz , Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 29(2012) 35
[03] C. Gui, M. Zhao, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Available online 9 May 2014, ISSN 0294-1449, http://dx.doi.org/10.1016/j.anihpc.2014.03.005.
[04] G. Nadin, Critical, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Available online 9 May 2014, ISSN 0294-1449, http://dx.doi.org/10.1016/j.anihpc.2014.03.007
[05] T. A. Davydova, A. I. Fishchuk, Ukrainian J Phys 1995;40:487-94.
[06] T. A. Davydova, A. I. Fishchuk, Phys Scripta 1998;57:118-26.
[07] Y. F. Chen, C. Y. Wang, S. H. Wang, I. A. Yu, Phys Rev Lett 2006;96:043603.
[08] X. Wang , D. Brown, K. Lindenberg, Phys Rev A 1988;37:3557-66.
[09] Kh. I. Pushkarov, D. I. Pushkarov, and I. V. Tomov: Opt. Quant. Electr. 11(1979) 471.
[10] J. M. Zhu and Z. Y. Ma: Chaos, Solitons & Fractals 33 (2007) 958.
[11] S. Tanev and D. I. Pushkarov: Opt. Commun. 141 (1997) 322.
[12] L. Gagnon: J. Opt. Soc. Am. A 6 (1989) 1477.
[13] H. W. Schürmann: Phys. Rev. E 54 (1996) 4312.
[14] Z. Birnbaum and B. A. Malomed: Physica D 237 (2008) 3252.
[15] J. Fujioka and A. Espinosa: J. Phys. Soc. Jpn. 65 (1996) 2440.
[16] S. L. Palacios: Chaos, Solitons & Fractals 19 (2004) 203.
[17] A. Milgram, J. of Theoretical Biology, (2011), 271, 157-158.
[18] J. Ghanouchi, H. Labiadh and K. Boubaker, Int. J. of Heat and Technology, 26 (2008), 49-53
[19] S. Slama, J. Bessrour, K. Boubaker, M. Bouhafs, Eur. Phys. J. Ap. Ph. 44, (2008), 317-322
[20] S. Slama, M. Bouhafs and K. B. Ben Mahmoud, Int. J. of Heat and Techn., 26(2), (2008),141-146.
[21] S. Lazzez, K.B. Ben Mahmoud, S. Abroug, F. Saadallah, M. Amlouk, Current Applied Physics, 9 (5), (2009) 1129-1133
[22] T. Ghrib, K. Boubaker and M. Bouhafs, Modern Physics Letters B, 22 (2008) 2893-2907
[23] S. Fridjine, K.B. Ben Mahmoud, M. Amlouk, M. Bouhafs, Journal of Alloys and Compounds, 479 (2009) (1-2), 457-461
[24] C. Khélia, K. Boubaker, T. Ben Nasrallah, M. Amlouk, S. Belgacem, Journal of Alloys and Compounds, 477(1-2) (2009) 461-467
[25] K.B. Ben Mahmoud, M. Amlouk, Materials Letters, 2009, 63 (12), 991-994
[26] M. Dada, O.B. Awojoyogbe, K. Boubaker, Current Applied Physics, Volume 9, Issue 3 (2009) 622-624.
[27] S. Tabatabaei, T. Zhao, , O. Awojoyogbe, F. Moses, Int.J. Heat Mass Transfer, 45 (2009) 1247-1255.
[28] A. Belhadj, J. Bessrour, M. Bouhafs, L. Barrallier, J. of Thermal Analysis and Calorimetry, 2009, 97, 911-920.
[29] A. Belhadj, O. Onyango, N. Rozibaeva, J. Thermophys. Heat Transf. , 23 (2009) 639-642.
[30] P. Barry, A. Hennessy, Journal of Integer Sequences, 13 (2010),1-34.
[31] M. Agida, A. S. Kumar, El. Journal of Theoretical Physics, 7, (2010) 319-326.
[32] A. Yildirim, S. T. Mohyud-Din, D. H. Zhang, Computers and Mathematics with Applications, 59 (2010) 2473-2477.
[33] A. S. Kumar, Journal of the Franklin Institute, 2010, 347, 1755-1761.
[34] S. Fridjine, M. Amlouk, Modern Phys. Lett. B, 23 (2009) 2179-2182
[35] M. Benhaliliba, Benouis, C.E. Boubaker, K. Amlouk M. Amlouk, A. A New Guide To Thermally Optimized Doped Oxides Monolayer Spray-grown Solar Cells: The Amlouk-boubaker Optothermal Expansivity ψab in the book: Solar Cells - New Aspects and Solutions, Edited by: Leonid A. Kosyachenko, [ISBN 978-953-307-761-1, by InTech], (2011) 27-41.
[36] H. Rahmanov, Studies in Nonlinear Sciences, 2 (1) (2011) 46-49.
[37] N. Fabien II, M. Alidou, K. T. Crépin. Modulational instability in the cubic–quintic nonlinear Schrödinger equation through the variational approach. Optics Commun 2007; 275(2):421-8.
[38] V. E. Zakharov, E. A. Kuznetsov. Optical solitons and quasisolitons. Sov Phys JETP 1998; 86: 1035-46.
[39] G. S. Agarwal and S. D. Gupta: Phys. Rev. A 38 (1988) 5678.
[40] J. Fujioka and A. Espinosa: J. Phys. Soc. Jpn. 66 (1997) 2601.
[41] C. Liu, Computer Physics Communications, 181, (2010) 317-324
[42] S. Liang, D. J. Jeffrey, Computer Physics Communications, 180 ( 2009) 1429-1433
[43] S. Liang, D. J. Jeffrey, Computer Physics Communications, 178 (2008) 700-712
[44] T. Khang Nguyen, F. Rotermund, I. Park, A traveling-wave stripline dipole antenna on a substrate lens at terahertz frequency, Current Applied Physics, 14( 8) 2014, s 998-1004
600 ATLANTIC AVE, BOSTON,
MA 02210, USA
+001-6179630233
AIS is an academia-oriented and non-commercial institute aiming at providing users with a way to quickly and easily get the academic and scientific information.
Copyright © 2014 - 2017 American Institute of Science except certain content provided by third parties.