The Energy Eigenvalues of Dirac Equation with the Modified
Eckart and Modified Deformed Hylleraas Potential
by Shape Invariance Approach¹

S. Arbabi Moghadam^a, H. Mehraban^b, and H. Habibi Khoshmehr^c

^aYoung Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

^bPhysics Department, Faculty of Sciences, Semnan University, Semnan, Iran

^cDepartment of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

e-mail: sah.arbabi.yrec@iauctb.ac.ir, arbabimo@ualberta.ca

Abstract—By using the supersymmetry quantum mechanics method, we approximately solve the Dirac equa-
tion for the modified Eckart potential and the modified deformed Hylleraas including Coulomb-like tensor
potential under spin and pseudospin symmetry. We obtained approximate energy eigenvalues and the corre-
sponding wave functions in terms of the Jacobi polynomial under the spin and pseudospin symmetries limit. In
order to test the accuracy of our work, we compared our numerical results with that Nikiforov-Uvarov (NU)
method. This shows that our results are consistent with those found in the literature.

Keywords: Dirac equation, spin and pseudospin symmetry, SUSY, Coulomb-like tensor potential, modified
Eckart, modified deformed Hylleraas

DOI: 10.1134/S154747711505009X

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