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

Hossein Rahbar

doi:doi:10.11648/j.ijtam.20160201.12

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

Hossein Rahbar

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 1)

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), 2024. Published by Science Publishing Group

Keywords

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

References

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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

Hossein Rahbar

Department of Physics, Faculty of science, University of Mazandaran, Babolsar, Iran

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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

Copy | Download

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}
}

Copy | Download

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  -

Copy | Download