Abstract
In this paper, the solutions of the D+1-dimensional Dirac equation in the presence of the Morse potential are investigated by using the supersymmetric quantum mechanics and shape invariance theory with spin symmetry. The bound state energy spectrum and the ground state wave function are calculated by supersymmetry approach. Also, it is shown that the energy spectrum and vibrational energy eigenvalue at the critical point can be obtained by a numerical method which is called the asymptotic iteration method. The $$X^2\Sigma ^+$$ state of the CP and $$X^1\Sigma ^+$$ state of the $$SiF^+$$ molecules are considered, and their relativistic energy eigenvalues are studied.
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