volume | PIER Journals

Abstract

A new mathematical method and proposal for generation of shape invariant potentials using supersymmetric quantum mechanics is introduced. For this purpose the potential term in the Schrodinger equation is expressed in terms of the super potential. The obtained equation transformed into well known ordinary second order differential equation. Using standard technique, the Nikiforov-Uvarov (NU) method the superpotential in the Schrodinger equation is expressed in terms of the parameters appeared in the NU-approach concluding to a nonlinear differential equation. By solving the obtained equation and using relation between superpotential and potential the shape invariant potentials are obtained. The proposed method is general and straightforward for introducing of the shape invariant potentials.

1. Fayet, P. and S. Ferrara, Supersymmetry in Physics, 1985.

2. Witten, E., Nucl. Phys. B, Vol. 188, 513, 1981.
doi:10.1016/0550-3213(81)90006-7

3. Cooper, F., A. Khare, and U. Sukhatme, Supersymmetry in Quantum Mechanics, World Scientific, 2001.

4. Gel'fand, Y. A. and E. P. Likhtman, JETP Lett., Vol. 13, 323, 1971.

5. Ramond, P., Phys. Rev. D, Vol. 3, 2415, 1971.
doi:10.1103/PhysRevD.3.2415

6. Volkov, D. and V. Akulov, Phys. Lett. B, Vol. 46, 109, 1973.

7. Wess, J. and B. Zumino, Nucl. Phys., Vol. 70, 39, 1974.
doi:10.1016/0550-3213(74)90355-1

8. Fayet, P. and S. Ferrara, Phys. Rep., Vol. 32, 249, 1977; M. F. Sohnius, Phys. Rep., Vol. 128, 39, 1985.
doi:10.1016/0370-1573(77)90066-7

9. Cooper, F. and B. Freedman, Ann. Phys., Vol. 146, 262, 1983.
doi:10.1016/0003-4916(83)90034-9

10. Bender, C., F. Cooper, and A. Das, Phys. Rev. D, Vol. 28, 1473, 1983.
doi:10.1103/PhysRevD.28.1473

11. Gates, Jr., S. J., M. Grisaru, M. Rocek, and W. Siegel, Superspace or One Thousand and One Lessons in Supersymmetry, Benjamin/Cummings, Reading, Mass., 1983.

12. Green, M. B., J. Schwarz, and E. Witten, Superstring Theory, Cambridge, 1987.

13. Cooper, F., A. Khare, and U. Sukhatme, "Supersymmetry and quantum mechanics," Phys. Rep., Vol. 251, 267, 1995.
doi:10.1016/0370-1573(94)00080-M

14. Cooper, F., J. N. Ginocchio, and A. Khare, Phys. Rev. D, Vol. 36, 356, 1983.

15. Nikiforov, A. F. and V. B. Uvarov, "Special functions of mathematical physics ," Birkhauser, Basel, 1988.

16. Aktas, M. and R. Sever, "Exact supersymmetric solution of Schrodinger equation for central confining potentials by using the Nikiforov-Uvarov method ," J. Mol. Struct. Theochem, Vol. 710, 223, 2004.
doi:10.1016/j.theochem.2004.09.011

17. Berkdemir, A., C. Berkdemir, and J. Han, "Bound state solutions of the Schrodinger equation for modified Kratzer's molecular potential ," Chem. Phys. Lett., Vol. 417, 326, 2006.
doi:10.1016/j.cplett.2005.10.039

18. Berkdemir, C., A. Berkdemir, and R. Sever, "Systematical approach to the exact solutions of the Dirac equation for a deformed form of the Woods-Saxon potential," J. Phys. A: Math. Gen., Vol. 39, 13455, 2006.
doi:10.1088/0305-4470/39/43/005

19. Yasuk, F., A. Durmus, and I. Boztosun, "Exact analytical solution to the relativistic Klein-Gordon equation with non-central equal scalar and vector potentials," J. Math. Phys., Vol. 47, 082302, 2006.
doi:10.1063/1.2227258

20. Egrifes, H. and R. Sever, "Bound state of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method," Phys. Lett. A, Vol. 344, 117, 2005.
doi:10.1016/j.physleta.2005.06.061

21. Simsek, M. and H. Egrifes, "The Klein-Gordon equation for the generalized Hulthen potential in complex quantum mechanics," J. Phys. A: Math. Gen., Vol. 37, 4379, 2004.
doi:10.1088/0305-4470/37/15/007

22. Bayrak, O. and I. Boztosun, "Analytical solution to the Hulthen and Morse potentials by using the asymptotic iteration method," J. Mol. Struct. Theochem, Vol. 802, 17, 2007.
doi:10.1016/j.theochem.2006.09.006

23. Yasuk, F., C. Berkdemir, and A. Berkdemir, "Exact solutions of the Schrodinger equation with non-central potential by the Nikiforov-Uvarov method ," J. Phys. A: Math. Gen., Vol. 38, 6579, 2005.
doi:10.1088/0305-4470/38/29/012

25. Yasiltas, O., "PT/non-PT symmetric and non-Hermitian Poschl-Teller-like solvable potentials Nikiforov-Uvarov method," Phys. Scr., Vol. 75, 41, 2007.
doi:10.1088/0031-8949/75/1/006

25. Hatamzadeh-Varmazyar, S. and M. Naser-Moghadasi, "New numerical method for determining the scattered electromagnetic fields from thin wires," Progress In Electromagnetics Research B, Vol. 3, 207-218, 2008.
doi:10.2528/PIERB07121303

26. Banai, A. and A. Hashemi, "A hybrid multimode contour integral method for analysis of the H-plane waveguide discontinuties," Progress In Electromagnetics Research, Vol. 81, 167-182, 2008.
doi:10.2528/PIER07122601

27. Ho, M., F.-S. Lai, S.-W. Tan, and P.-W. Chen, "Numerical simulation of propagation of EM pulse through lossless nonuniform dielectric slab using characteristic-based method ," Progress In Electromagnetics Research, Vol. 81, 197-212, 2008.
doi:10.2528/PIER08010303

28. Collino, F., F. Millot, and S. Pernet, "Boundary-integral methods for iterative solution of scattering problems with variable impedance surface condition ," Progress In Electromagnetics Research, Vol. 80, 1-28, 2008.
doi:10.2528/PIER07103105

29. Carpentieri, B., "Fast iterative solution methods in electromagnetic scattering," Progress In Electromagnetics Research , Vol. 79, 151-178, 2008.
doi:10.2528/PIER07100802

30. Singh, V., Y. Prajapati, and J. P. Saini, "Modal analysis and dispersion curves of a new unconventional Bragg waveguide using a very simple method ," Progress In Electromagnetics Research, Vol. 64, 191-204, 2006.
doi:10.2528/PIER06071101

31. Khalaj-Amirhosseini, M., "Analysis of lossy inhomogeneous planar layers using equivalent sources method," Progress In Electromagnetics Research, Vol. 72, 61-73, 2007.
doi:10.2528/PIER07030802

32. Berginc, G. and C. Bourrely, "The small-slope approximation method applied to a three-dimensional slab with rough boundaries," Progress In Electromagnetics Research, Vol. 73, 131-211, 2007.
doi:10.2528/PIER07030806

33. Kazemi, S., H. R. Hassani, G. Dadashzadeh, and F. Geran, "Performance improvement in amplitude synthesis of unequally spaced array using least mean square method ," Progress In Electromagnetics Research B, Vol. 1, 135-145, 2008.
doi:10.2528/PIERB07103002

34. Samuel, E. P. and D. S. Patil, "Analysis of wavefunction distribution in quantum well biased laser diode using transfer matrix method," Progress In Electromagnetics Research Letters, Vol. 1, 119-128, 2008.
doi:10.2528/PIERL07111902

Dr. Hossein Motavali

Prof. Ali Rostami