Abstract
This work is based on deploying the algorithm of the second-order supersymmetric quantum mechanics to the spin $$\frac{1}{2}$$ particle behavior in a cosmic sting spacetime. The spectral equivalence of the different systems may shed a light on the quantum mechanics for the topological defects. From this point of view, we have obtained the solutions of the new generated potentials which are free of singularities. Moreover, $$\hbox {SO}(2,1)$$ Lie algebraic approach is constructed for the intertwining relation.
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