Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method
American Journal of Physical Chemistry
Volume 4, Issue 5, October 2015, Pages: 38-41
Received: Aug. 25, 2015;
Accepted: Sep. 6, 2015;
Published: Oct. 20, 2015
Views 3483 Downloads 96
Akaninyene D. Antia, Theoretical Physics Group, Department of Physics, Faculty of Science, University of Uyo, Uyo, Akwa Ibom State, Nigeria
We have solved the non-relativistic Schrödinger equation with Scarf II plus Rosen-Morse II potential analytically for arbitrary l-state by using the newly improved ansaltz for the wave function and adopting the modified approximation scheme to evaluate the centrifugal term. The bound state energy spectrum and the un-normalized wave function expressed in terms of Jacobi polynomial are also obtained. With this method, we have obtained a negative energy spectrum for the system.
Akaninyene D. Antia,
Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method, American Journal of Physical Chemistry.
Vol. 4, No. 5,
2015, pp. 38-41.
L. Z. Yi, Y. F. Diao, J. Y. Liu, C. S. Jia. Bound state of the Klein-Gordon equation with vector and scalar Rosen-Morse type potentials. Physics Letter A, Vol. 333, 212, 2004.
A. N. Ikot. Analytical solutions of Schrodinger equation with generalized hyperbolic potential using Nikiforov-Uvarov method. African Review of Physics, Vol. 6, No. 0026, pp. 221-228, 2011.
A. D. Antia, I. E. Essien, E. B. Umoren, C. C. Eze. Approximate solutions of the non-relativistic Schrodinger equation with inversely quadratic Yukawa plus Mobius square potential via parametric Nikiforov-Uvarov method. Advances in Physics Theories and Applications, Vol. 44, pp.1-13, 2015.
A. D. Antia, I. O. Akpan, A. O. Akankpo.Relativistic treatment of spinless particles subject to modified Scarf II potential. International Journal of High Energy Physics, Vol. 2, No.4, pp.50-55, 2015.
A. D. Antia, A. N. Ikot, E. E. Ituen, I. O. Akpan. Bound state solutions of the Klein-Gordon equation for deformed Hulthen potential with position dependent mass. Sri Lankan Journal of Physics, Vol. 13, No. 1, pp. 27-40, 2012.
H. Hassanabadi, S. Zarrinkamar and A. A. Rajabi. Exact solutions of D-dimensional Schrodinger equation for energy-dependent potential by Nikiforov-Uvarov method. Communications in Theoretical Physics, Vol. 55, 541, 2011.
W. C. Qiang and S. H. Dong. The Manning-Rosen potential studied by a new approximation scheme to the centrifugal term. Physica Scripta, Vol. 79, 045004, 2009.
A. D. Antia, A. N. Ikot, H. Hassanabadi and E. Maghsoodi. Bound state solutions of Klein-Gordon equation with Mobius square plus Yukawa potentials. Indian Journal of Physics, Vol. 87, No. 11, pp.1133-1139, 2013.
G. F. Wei, C. Y. Long and S. H. Dong. The scattering of the Manning-Rosen potential with centrifugal term. Physica Scripta, Vol. 77, 035001, 2008.
S. Dong, S. H. Garcia-Ravalo and S. H. Dong. Quantization rule solution to the Hulthen potential in arbitrary l-state. Physica Scripta, Vol. 76, 393, 2007.
J. Lu. Approximate spin and pseudospin solutions of the Dirac equation. Physica Scripta, Vol. 72, 349, 2005.
R. L. Greene and C. Aldrich. Variational wave functions for a screened coulomb potential. Physical Revision A, Vol. 14, 2363, 1976.
C. S. Jia, T. Chen and L. G. Cui. Approximate analytical solutions of the Dirac equation with the generalized Poschl-Teller potential including the pseudo-spin centrifugal term. Physics Letter A, Vol. 373, pp.1621-1626, 2009.
E. H. Hill. The theory of vector spherical harmonics. American Journal of Physics, Vol. 22, pp.211-221, 1954.
F. Yasuk and M. K. Bahar. Approximate solutions of the Dirac equation with position-dependent mass for the Hulthen potential by the asymptotic iteration method. Physica Scripta, Vol. 85, 045004, 2012.
H. Hassanabadi, E. Maghsoodi and S. Zarrinkamar. Relativistic symmetries of Dirac equation and the Tietz potential. European Physics Journal Plus, Vol. 127, 31, 2012.
M. Bag, M. M. Panja, R. Dutt and Y. P. Varshni. Modified shifted large-N approach to the Morse potential. Physical Review A, Vol. 46, pp. 6059-6065, 1992.
A. D. Antia, E. E. Ituen, H. P. Obong and C. N. Isonguyo. Analytical solutions of the modified coulomb potential using the factorization method. International Journal Recent advances in Physics, Vol. 4, No. 1, pp.55-65, 2015.
S. M. Ikhdair and R. Sever. Exact polynomial eigen solution of Schrodinger for pseudo harmonics potential. International Journal of Modern Physics, Vol.19, pp.221-229, 2008.
A. F. Nikiforov and V. B. Uvarov. Special Functions of mathematical Physics (Basel: Birkhauser), 1988.
A. N. Ikot. Solutions of the Klein-Gordon equation with equal scalar and vector modified Hylleraas plus exponential Rosen-Morse potential. Chinese Physics Letter, Vol. 29, 060307, 2012.
H. Hassanabadi, B. H. Yazarlo, S. Zarrinkamar and A. A. Rajabi. Duff-Kemmer-Petiau equation under a scalar Coulomb interaction. Physics Revision C, Vol. 84, 064003, 2011.
A. N. Ikot, L. E. Akpabio and E. B. Umoren. Exact solution of Schrodinger equation with inverted Woods-Saxon and Manning-Rosen potential. Journal of Scientific Research, Vol. 3, No. 1, pp. 25-33, 2011.
L. D. Landau and E. M. Lifshitz. Quantum Mechanics, Non-relativistic Theory (Canada: Pergamon), 1977.
L. I. Schiff. Quantum Mechanics (New York: McGraw Hill), 1955.
A. D. Polyanin and A. V. Manzhirov. Handbook of integrals equation (CRC press Boca Rotan), doi: 10.1201/9781420050066, 1998.
M. R. Pahlavai, J. Sadeghi and M. Ghezelbash. Applied Science, Vol. 11, 106, 2009.
K. M. Khanna, G. F. Kanyeki, S. K. Rotich, P. K. Torongey and S. E. Ameka. Indian Journal Pure and Applied Physics, Vol. 48, 7, 2010.