Approximate Solutions of the Schrodinger Equation for a Momentum-Dependent potential

Clement Onate; I. B. Okon; M. C. Onyeaju; A. D.   Antia

doi:10.46481/jnsps.2022.653

Authors

C. A. Onate
[email protected]
Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria; Landmark University SDG 4 (Quality Education)
I. B. Okon Theoretical Physics Group, Department of Physics, University of Uyo, Nigeria
M. C. Onyeaju Department of Physics, University of Port Harcourt, Choba, Nigeria
A. D. Antia Theoretical Physics Group, Department of Physics, University of Uyo, Nigeria

Keywords:

Eigensolutions, wave equation, potential models, momentum dependent

Abstract

The solution of one-dimensional Schrodinger equation for a newly proposed potential called modified shifted Deng-Fan momentum-dependent potential is obtained via supersymmetric approach. The expectation values of momentum and position were calculated using Hellmann Feynman Theorem. The effects of momentum-dependent parameter on the solutions of the system as well as the expectation values were studied. Finally, the special cases of the interacting potential were obtained.

Dimensions

REFERENCES

L. I. Schiff, “Quantum Mechanics 3rd edn”, New York: McGraw-Hill (1968).

S. Flugge, “Practical Quantum mechanics”, Berlin Springer (1974).

S. H. Dong & A. Gonzalez-Cisnero, “Energy spectra of the hyperbolic and Second P¨oschl-Teller like potentials solved by new exact quantization rule”. Annals of Physics 323 (2008) 1136.

C. A. Onate, K. J. Oyewumi & B. J. Falaye, “Approximate solutions of the Schr¨odinger equation with hyperbolical potential: Supersymmetric Approach”, Few-Body Systems 55 (2014) 61.

X. Y. Gu, S. H. Dong & Z. Q. Ma, “Energy spectra for modified Rosen-Morse potential solved by the exact quantization rule”, Journal of Physics A: Mathematical and Theoretical 42 (2009) 035303.

S. M. Ikhdair & J. Abu-Hasna, “Quantization rule solution to the Hulth`en potential in arbitrary dimensions with a new approximation scheme for the centrifugal term”, Physical Scripta 83 (2011) 025002.

O. Bayrak & I. Boztosun, “Bound state solutions of the Hulth´en potential by using the asymptotic iteration method”, Physica Scripta 76 (2007) 92.

S. M. Ikhdair, “On the bound state solutions of the Manning-Rosen potential including an improved approximation to the orbital centrifugal term”, Physica Scripta 83 (2011) 015010.

M. C. Zhang & B. An, “Analytical solutions of the Manning-Rosen potential in the Tridiagonal program”, Chinese Physics Letters 27 (2010) 110301.

R. H. Hammed, “Approximate solutions of the Schr¨odinger equation with Manning-Rosen potential in two dimensions by using the shifted 1/N expansion method”, Journal of Basrah Research 38 (2012) 51.

O. Bayrak, I. Boztosun & H. Ciftci, “Exact analytical solutions to the Kratzer potential by the asymptotic iteration method”, International Journal of Quantum Chemistry 187 (2007) 540.

M. Aygun, O. Bayrak & I. Boztosun, “Solutions of the radial Schrodinger equation for the potential family using the asymptotic iteration method”, Journal of Physics B: Atomic, Molecular and Optical Physics 40 (2007) 537.

C. A. Onate, M. C. Onyeaju, A. N. Ikot, O. Ebomwonyi & J. O. A. Idiodi, “Fisher information and Uncertainty relations for potential family”, International Journal of Quantum Chemistry 119, e25991, (2019).

A. D. Alhaidari, “Solutions of the nonrelativistic wave equation with position-dependent effective mass”, Physica Review A 66 (2002) 042116.

J. Yu, S. H. Dong & G. H. Sun, “Series solutions of the Schrodinger equation with position-dependent mass for the Morse potential”, Physics Letters A 322 (2004) 290.

R. J. Lombard, J. Mareo & C. Volpe, “Wave equation with energy dependent potentials for confined systems”, Journal of Physics G: Nuclear and Particle Physics 34 (2007) 1879.

C. S. Jia, Y.-F. Diao & X. L. Liu, “Equivalence of the Wei potential model and Tietz potential model for diatomic molecules”, Journal of Chemical Physics 137 (2012) 01410.

L.-H. Zhang, X.-P. Li & C.-S. Jia, “Approximate Solutions of the

Schr¨odinger Equation with the Generalized Morse Potential Model Including the Centrifugal Term”, International Journal of Quantum Chemistry 111 (2011) 1870.

C. A. Onate, A. N. Ikot, M. C. Onyeaju, O. Ebomwonyi & J. O. A. Idiodi, “Effect of dissociation energy on Shannon and Renyi entropies”, Karbala International Journal of Modern Science 4 (2018) 134.

W.-C. Qiang & S.-H. Dong, “Analytical approximations to the solutions of the Manning–Rosen potential with centrifugal term”, Physics Letters A 368 (2007) 13.

C. A. Onate, G. O. Egharevba & D. T. Bankole, “Eigensolution to Morse potential for scandium and nitrogen monoiodides”, Journal of Nigerian Society of Physical Sciences 3 (2021) 282.

C. Tezcan & S. A. Sever, “A General Approach for the Exact Solution of the Schr¨odinger Equation”, Internation Journal of Theoretical Physics 48 (2008) 337.

G. Hellmann, “Einfuhrung in die Quantenchemie”, Denticke, Vienna (1937).

R. P. Feynman, “Forces in Molecules”, Physica Review 56 (1939) 340.

K. J. Oyewumi, “Analytical solutions of the Kratzer-Fues potential in an arbitrary number of dimensions”, Foundations in Physics Letters 18 (2005) 75.

D. Popov, “Barut-Girardello coherent states of the pseudoharmonic oscillator”, Journal of Physics A: Mathematical and General 34 (2001) 5283.

H. Hassanabadi, B. H. Yazarloo, & L. L. LU, “Approximate Analytical Solutions to the Generalized P¨oschl—Teller Potential in D Dimensions”, Chinese Physics Letters 29 (2012) 020303.

S. –H. Dong & X. –Y. Gu, “Arbitrary l-state solutions of the Schr¨odinger equation with the Deng-Fan molecular potential”, Journal of Physics: Conference series 96 (2008) 012109.

O. Bayrak & I. Boztosun, “Bound state solutions of the Hulth`en potential by using asymptotic iteration method”, Physica Scripta 76 (2007) 92.

Y. P. Varshni, “Eigen-energies and oscillator strengths for the Hulth`en potential”, Physical Review A 41 (1990) 4682.