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Schrödinger Equation with Double- Cosine and Sine – Squared Potential by Darboux Transformation Method and Supersymmetry

Received: 6 September 2016     Accepted: 26 September 2016     Published: 14 October 2016
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Abstract

On this paper the one-dimensional Schrödinger equation for the double cosine and sine- squared potential is considered. Here, we construct the first order Darboux transformation and the real valued condition of transformed potential for two corresponding equations. In that case we obtain the transformed of potential and wave function and finally, investigate the supersymmetry aspect of such corresponding equation. Also we show that the first order equation is satisfied by commutative and anti-commutative algebra with the α constant condition at different limit for the χ.

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 1)
DOI 10.11648/j.ijtam.20160201.12
Page(s) 7-12
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

Double-Cosine Potential, Sine-Squared Potential Darboux Transformation, Supersymmetry, Shape Invariance Potential

References
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[19] O. A. Choustova, Quantum Bohmian model for _nancial markets, Physica A 374(2007) 304.
[20] Morales J, Pena JJ, Lopez- Bonilla JL. Generalization the Darboux transform. J Math Phys 2001; 42: 966-75.
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  • APA Style

    Hossein Rahbar. (2016). Schrödinger Equation with Double- Cosine and Sine – Squared Potential by Darboux Transformation Method and Supersymmetry. International Journal of Theoretical and Applied Mathematics, 2(1), 7-12. https://doi.org/10.11648/j.ijtam.20160201.12

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    ACS Style

    Hossein Rahbar. Schrödinger Equation with Double- Cosine and Sine – Squared Potential by Darboux Transformation Method and Supersymmetry. Int. J. Theor. Appl. Math. 2016, 2(1), 7-12. doi: 10.11648/j.ijtam.20160201.12

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    AMA Style

    Hossein Rahbar. Schrödinger Equation with Double- Cosine and Sine – Squared Potential by Darboux Transformation Method and Supersymmetry. Int J Theor Appl Math. 2016;2(1):7-12. doi: 10.11648/j.ijtam.20160201.12

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  • @article{10.11648/j.ijtam.20160201.12,
      author = {Hossein Rahbar},
      title = {Schrödinger Equation with Double- Cosine and Sine – Squared Potential by Darboux Transformation Method and Supersymmetry},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {2},
      number = {1},
      pages = {7-12},
      doi = {10.11648/j.ijtam.20160201.12},
      url = {https://doi.org/10.11648/j.ijtam.20160201.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160201.12},
      abstract = {On this paper the one-dimensional Schrödinger equation for the double cosine and sine- squared potential is considered. Here, we construct the first order Darboux transformation and the real valued condition of transformed potential for two corresponding equations. In that case we obtain the transformed of potential and wave function and finally, investigate the supersymmetry aspect of such corresponding equation. Also we show that the first order equation is satisfied by commutative and anti-commutative algebra with the α constant condition at different limit for the χ.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Schrödinger Equation with Double- Cosine and Sine – Squared Potential by Darboux Transformation Method and Supersymmetry
    AU  - Hossein Rahbar
    Y1  - 2016/10/14
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ijtam.20160201.12
    DO  - 10.11648/j.ijtam.20160201.12
    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
    SP  - 7
    EP  - 12
    PB  - Science Publishing Group
    SN  - 2575-5080
    UR  - https://doi.org/10.11648/j.ijtam.20160201.12
    AB  - On this paper the one-dimensional Schrödinger equation for the double cosine and sine- squared potential is considered. Here, we construct the first order Darboux transformation and the real valued condition of transformed potential for two corresponding equations. In that case we obtain the transformed of potential and wave function and finally, investigate the supersymmetry aspect of such corresponding equation. Also we show that the first order equation is satisfied by commutative and anti-commutative algebra with the α constant condition at different limit for the χ.
    VL  - 2
    IS  - 1
    ER  - 

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Author Information
  • Department of Physics, Faculty of science, University of Mazandaran, Babolsar, Iran

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