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We study the solution of the relativistic Schr\"odinger equation for a pointparticle in 1-d under $\delta$-function potential by using cutoffregularization. We show that the problem is renormalizable, and the results areexactly the same as the ones obtained using dimensional regularization.

A Solution of the Relativistic Schr\"odinger Equation for the $\delta$-Function Potential in 1-dimensiona with Cutoff Regularization