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

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